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• Steps

To find the equation of a line, you need to two things: a) a point on that line; and b) its slope (sometimes referred to as slope) coefficient. But depending on the case, the way to find this information and what you can then manipulate with it may vary. For the sake of simplicity, this article will focus on equations of the coefficients form and the degree of the degree of origin y = mx + b instead of the form of the slope and a point on a line (y - y₁) = m (x - x₁).

Steps

Method 1 of 5: General information

1. Know what you're looking for. Before you start looking for an equation, make sure you have a good understanding of what you're trying to find. Pay attention to the following statements:
   • Points are determined with these paired pairs like (-7, -8) or (-2, -6).
   • The first number in the ranked pair is diaphragm degrees. It controls the horizontal position of the point (whether to the left or to the right from the origin).
   • The second number in the ranked pair is toss. It controls the vertical position of the point (how much above or below the origin).
   • Slope between two points is defined as "straight across the horizontal" - in other words, how far you have to go up (or down) and to the right (or to the left) to move from point to point. the other point of the line.
   • Two straight lines parallel if they do not intersect.
   • Two straight lines perpendicular to each other if they intersect and form a right angle (90 degrees).
2. Determine the type of problem.
   • Know the coefficient of angles and a point.
   • Knowing two points on the line, but not the coefficient of the angle.
   • Know a point on the line and another line that is parallel to the line.
   • Know a point on the line and another line perpendicular to that line.
3. Solve the problem using one of the four methods shown below. Depending on the information given, we have different solutions. advertisement

Method 2 of 5: Know the coefficients of angles and a point on the line

1. 

   
   
   Calculate the square of the origin in your equation. Tung degree (or variable b in the equation) is the intersection point of the line and the vertical axis. You can calculate the toss of the origin by rearranging the equation, and finding b. Our new equation looks like this: b = y - mx.
   • Enter the angular coefficients and coordinates in the above equation.
   • Multiplying the angle factor (m) with the coordinate of the given point.
   • Get the intersection of the point minus the point.
   • You have found it b, or toss the origin of the equation.

2. 

   
   
   Write the formula: y = ____ x + ____ , the same white space.

3. 

   Fill the first space, preceded by x, with the coefficient of the angle.

4. 

   
   
   Fill in the second space with the vertical offset that you just calculated.

5. 

   Solve the example problem. "Find the equation for a line that passes through the point (6, -5) and has a coefficient of 2/3."
   • Rearrange the equation. b = y - mx.
   • Substitute value and solve.
     • b = -5 - (2/3) 6.
     • b = -5 - 4.
     • b = -9
   • Double check if your offset is really -9 or not.
   • Write the equation: y = 2/3 x - 9
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Method 3 of 5: Know two points lying on a line

1. Calculate the coefficient of the angle between the two points. The coefficient of the angle is also known as the "straightness over the horizontal" and you can imagine it is the description that shows how much when the line went up or down one unit to the left or right. The equation for the slope is: (Y₂ - Y₁) / (X₂ - X₁)
   • Use two known points and replace them in the equation (The two coordinates here are two values y and two values x). It doesn't matter which coordinate to put first, as long as you are consistent in your posture. Here are a few examples:
     • Point (3, 8) and (7, 12). (Y₂ - Y₁) / (X₂ - X₁) = 12 - 8/7 - 3 = 4/4, or 1.
     • Point (5, 5) and (9, 2). (Y₂ - Y₁) / (X₂ - X₁) = 2 - 5 / 9 - 5 = -3/4.

2. 

   Choose a pair of coordinates for the rest of the problem. Cross out the other pair of coordinates or hide them so you don't accidentally use them.

3. 

   Calculate the square root of the equation. Again, rearrange the formula y = mx + b so that b = y - mx. The same equation remains, you just transformed it a little bit.
   • Generate the number of angles and coordinates in the above equation.
   • Multiplying the angle factor (m) with the coordinate of the point.
   • Get the intersection of the point minus the point above.
   • You just found it b, or toss the original.

4. 

   Write the formula: y = ____ x + ____ ', including spaces.

5. 

   Enter the coefficient of the corner in the first space, preceded by x.

6. 

   Fill in the origin in the second space.

7. 

   Solve the example problem. "Given two points (6, -5) and (8, -12). Find the equation for the line that goes through the above two points."
   • Find the coefficient of the angle. Angular coefficient = (Y₂ - Y₁) / (X₂ - X₁)
     • -12 - (-5) / 8 - 6 = -7 / 2
     • The coefficient of the angle is -7/2 (From the first point to the second point, we go down 7 and right 2, so the coefficient of the angle is - 7 to 2).
   • Rearrange your equations. b = y - mx.
   • Number substitution and solution.
     • b = -12 - (-7/2) 8.
     • b = -12 - (-28).
     • b = -12 + 28.
     • b = 16
     • Note: When placing the coordinates, since you used 8, you also have to use -12. If you use 6, you'll have to use -5.
   • Double check to make sure your pitch is actually 16.
   • Write the equation: y = -7/2 x + 16
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Method 4 of 5: Know a point and a line are parallel

1. Determine the slope of the parallel line. Remember that the slope is a coefficient of x still y then there is no coefficient.
   • In the equation y = 3/4 x + 7, the slope is 3/4.
   • In the equation y = 3x - 2, the slope is 3.
   • In the equation y = 3x, the slope remains 3.
   • In the equation y = 7, the slope is zero (because the problem has no x).
   • In the equation y = x - 7, the slope is equal to 1.
   • In the equation -3x + 4y = 8, the slope is 3/4.
     • To find the slope of the equation above, we just need to rearrange the equation so that y stand alone:
     • 4y = 3x + 8
     • Divide two sides by "4": y = 3 / 4x + 2

2. 

   Calculate the intersection of the original using the slope of the angle you found in the first step and the equation b = y - mx.
   • Generate the number of angles and coordinates in the above equation.
   • Multiplying the angle factor (m) with the coordinate of the point.
   • Get the intersection of the point minus the point above.
   • You just found it b, toss the original.

3. 

   Write the formula: y = ____ x + ____ , include a space.

4. 

   Enter the coefficient of the angle found in step 1 in the first space, before x. The problem with parallel lines is that they have the same angular coefficients, so the starting point is also your end point.

5. 

   Fill in the origin in the second space.
6. Solve the same problem. "Find the equation for a line that goes through the point (4, 3) and is parallel to the line 5x - 2y = 1".
   • Find the coefficient of the angle. The coefficient of our new line is also the coefficient of the old line. Find the slope of the old line:
     • -2y = -5x + 1
     • Divide the sides by "-2": y = 5 / 2x - 1/2
     • The coefficient of the angle is 5/2.
   • Rearrange the equation. b = y - mx.
   • Number substitution and solution.
     • b = 3 - (5/2) 4.
     • b = 3 - (10).
     • b = -7.
   • Double-check to make sure -7 is the correct offset.
   • Write the equation: y = 5/2 x - 7
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Method 5 of 5: Know a point and a line perpendicular

1. Determine the slope of the given line. Please review the previous examples for more information.

2. 

   Find the opposite opposite of the slope. In other words, reverse the number and change the sign. The problem with two perpendicular lines is that they have opposite inverse coefficients. Therefore, you must transform the slope of the angle before using it.
   • 2/3 becomes -3/2
   • -6 / 5 becomes June 5
   • 3 (or 3/1 - same) becomes -1/3
   • -1/2 becomes 2

3. 

   Calculate the vertical degree of the slope in step 2 and the equation b = y - mx
   • Generate the number of angles and coordinates in the above equation.
   • Multiplying the angle factor (m) with the coordinate of the point.
   • Take the square of the point minus this product.
   • You have found it b, toss the original.

4. 

   Write the formula: y = ____ x + ____ ', include a space.

5. 

   Enter the slope calculated in step 2 in the first blank space, preceded by x.

6. 

   Fill in the origin in the second space.
7. Solve the same problem. "Given the point (8, -1) and the line 4x + 2y = 9. Find the equation for the line that goes through that point and is perpendicular to the given line".
   • Find the coefficient of the angle. The slope of the new line is the opposite inverse of the given coefficient of the slope. We find the slope of the given line as follows:
     • 2y = -4x + 9
     • Divide the sides by "2": y = -4 / 2x + 9/2
     • The coefficient of the angle is -4/2 good -2.
   • The opposite inverse of -2 is 1/2.
   • Rearrange the equation. b = y - mx.
   • Into the prize.
     • b = -1 - (1/2) 8.
     • b = -1 - (4).
     • b = -5.
   • Double check to make sure that -5 is the correct offset.
   • Write the equation: y = 1 / 2x - 5
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