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The intersection of two lines is the point at which the two lines meet. This point can be calculated by solving the linear equations that define the two lines. By finding the intersection of two lines, it is possible to calculate the slope of one line by using the equation of the other line. This is an important concept in mathematics that is used to determine the relationship between two lines.
You can use the following formulas to find the point of intersection of two straight lines in Google Sheets:
Find the X-Value of Intersection:
=(INTERCEPT(y2,x2)-INTERCEPT(y1,x1))/(SLOPE(y1,x1)-SLOPE(y2,x2))
This formula assumes x1 and x2 represent an array of x-values for each line and y1 and y2 represent an array of y-values for each line.
Once you find this x-value, you can then plug that value into this formula to find the y-value of intersection:
Find the Y-Value of Intersection:
=SLOPE(y1,x1)*x_intercept+INTERCEPT(y1,x1)
The following step-by-step example shows how to use these formulas in practice.
Step 1: Enter the Values for Each Line
First, let’s enter the (x, y) coordinates for two lines:
Step 2: Find the X-Value of Intersection
Next, type the following formula into cell B10 to find the x-value of intersection:
=(INTERCEPT(E3:E6,D3:D6)-INTERCEPT(B3:B6,A3:A6))/(SLOPE(B3:B6,A3:A6)-SLOPE(E3:E6,D3:D6))
The following screenshot shows how to use this formula in practice:
The x-value of intersection turns out to be 1.5.
Step 3: Find the Y-Value of Intersection
Next, type the following formula into cell B11 to find the y-value of intersection:
=SLOPE(B3:B6,A3:A6)*B10+INTERCEPT(B3:B6,A3:A6)
The following screenshot shows how to use this formula in practice:
The y-value of intersection turns out to be 3.
Step 4: Visualize the Intersection Point
If we plot each line on the same plot, we can see that the intersection point is indeed at the (x, y) coordinates of (1.5, 3):
This represents the point on the plot where the two lines intersect.