Content

• To step
• Method 1 of 3: Determine the intersection with the y-axis, using the slope
• Method 2 of 3: Using two points
• Method 3 of 3: Using an equation
• Tips

The y intercept of an equation is where the graph of an equation intersects with the y axis. There are several ways to find this intersection, depending on the information provided at the beginning of your assignment.

To step

Method 1 of 3: Determine the intersection with the y-axis, using the slope

1. Write down the slope. The slope of "y over x" is a single number that indicates the slope of a line. This type of problem also gives you the (x, y)coordinate of a point on the graph. If you don't have both of these details, continue with the other methods below.
   • Example 1: A straight line with slope 2 goes through the point (-3,4). Find the y-intersection of this line using the steps below.
2. Learn the usual form of a linear equation. Any straight line can be written as y = mx + b. When the equation is in this form, is m the slope and the constant b the intersection with the y axis.
3. Substitute the slope in this equation. Write down the linear equation, but instead of m you use the slope of your line.
   • Example 1 (continued):y = mx + b
     m = slope = 2
     y = 2x + b
4. Replace x and y with the coordinates of the point. If you have the coordinates of a point on the line, you can X and ycoordinates for the X and y in your linear equation. Do this for the comparison of your assignment.
   • Example 1 (continued): The point (3,4) is on this line. At this point, x = 3 and y = 4.
     Substitute these values ​​in y = 2X + b:
     4 = 2(3) + b
5. Solve for b. Do not forget, b is the y-intersection of the line. Now b the only variable is in the equation, rearrange the equation to solve this variable and find the answer.
   • Example 1 (continued):4 = 2 (3) + b
     4 = 6 + b
     4 - 6 = b
     -2 = b
     The intersection of this line with the y-axis is -2.
6. Record this as a coordinate. The intersection with the y axis is the point where the line intersects with the y axis. Because the y axis passes through the point x = 0, the x coordinate of the intersection with the y axis is always 0.
   • Example 1 (continued): The intersection with the y axis is at y = -2, so the coordinate point is (0, -2).

Method 2 of 3: Using two points

1. Write down the coordinates of both points. This method deals with problems where only two points are given on a straight line. Write down each coordinate in the form (x, y).
2. Example 2: A straight line passes through the points (1, 2) and (3, -4). Find the y-intersection of this line using the steps below.
3. Calculate the x and y values. The slope, or slope, is a measure of how much the line moves in the vertical direction for each step in the horizontal direction. You may know this as "y over x" (${ displaystyle { frac {y} {x}}}$Divide y by x to find the slope. Now that you know these two values, you can use them in "${ displaystyle { frac {y} {x}}}$Take another look at the standard form of a linear equation. You can describe a straight line with the formula y = mx + b, at which m is the slope and b the intersection with the y axis. Now we have the slope m and knowing a point (x, y), we can use this equation to calculate b (the intersection with the y-axis).
4. Enter the slope and the point in the equation. Take the equation in standard form and replace m by the slope you calculated. Replace the variables X and y by the coordinates of a single point on the line. It doesn't matter which point you use.
   • Example 2 (continued): y = mx + b
     Slope = m = -3, so y = -3x + b
     The line passes through a point with (x, y) coordinates (1,2), that is 2 = -3 (1) + b.
5. Solve for b. Now is the only variable left in the equation b, the intersection with the y axis. Rearrange equation such that b shown to one side of the equation, and you have your answer. Remember that the y-intersection point always has an x ​​coordinate of 0.
   • Example 2 (continued): 2 = -3 (1) + b
     2 = -3 + b
     5 = b
     The intersection with the y axis is (0.5).

Method 3 of 3: Using an equation

1. Write down the equation of the line. If you have the equation of the line, you can determine the intersection with the y-axis with a little algebra.
   • Example 3: What is the y-intersection of the line x + 4y = 16?
   • Note: Example 3 is a straight line. See the end of this section for an example of a quadratic equation (with a variable raised to the power of 2).
2. Substitute 0 for x. The y axis is a vertical line through x = 0. This means that every point on the y axis has an x ​​coordinate of 0, including the line's intersection with the y axis. Enter 0 for x in the equation.
   • Example 3 (continued): x + 4y = 16
     x = 0
     0 + 4y = 16
     4y = 16
3. Solve for y. The answer is the intersection of the line with the y axis.
   • Example 3 (continued): 4y = 16
     ${ displaystyle { frac {4y} {4}} = { frac {16} {4}}}$Confirm this by drawing a graph (optional). Check your answer by graphing the equation as precisely as possible. The point where the line passes through the y axis is the y axis intersection.
   • Find the y-intersection of a quadratic equation. A quadratic equation has one variable (x or y) raised to the second power.You can solve y using the same substitution, but because the quadratic equation is a curve, it can intersect the y axis at 0, 1, or 2 points. This means that you will end up with 0, 1 or 2 answers.
     • Example 4: To find the intersection of ${ displaystyle y ^ {2} = x + 1}$ with the y-axis, substitute x = 0 and solve for the quadratic equation.
       In this case, we can ${ displaystyle y ^ {2} = 0 + 1}$ solve by taking the square root of both sides. Remember that taking the square root square root gives you two answers: a negative answer and a positive answer.
       ${ displaystyle { sqrt {y ^ {2}}} = { sqrt {1}}}$
       y = 1 or y = -1. These are both intersection with the y-axis of this curve.

Tips

• Some countries use a c or any other variable for it b in the equation y = mx + b. However, its meaning remains the same; it's just a different way of notating.
• For more complicated equations, you can use the terms with y isolate on one side of the equation.
• When calculating the slope between two points, you can use the X and ysubtract coordinates in any order, as long as you put the point in the same order for both y and x. For example, the slope between (1, 12) and (3, 7) can be calculated in two different ways:
  • Second credit - first credit: ${ displaystyle { frac {7-12} {3-1}} = { frac {-5} {2}} = - 2.5}$
  • First point - second point: ${ displaystyle { frac {12-7} {1-3}} = { frac {5} {- 2}} = - 2.5}$