In this article, we will see how to find intersection of two linear straight lines with Excel. Most of us must have solved it with pen and paper during school days.

**To find intersection of two straight lines:**

- First we need the equations of the two lines.
- Then, since at the point of intersection, the two equations will have the same values of x and y, we set the two equations equal to each other. This gives an equation that we can solve for x
- We substitute that x value in one of the line equations and solve it for y

**Let the lines follow a system of linear equations :**

y1=m1x1+c1 and y2=m2x2+c2Where

m1: Gradient or Slope of line1,

c1: Intercept of line1,

m2: Gradient or Slope of line2,

c2: Intercept of line2

Let the point of intersection be s and t. They must satisfy the above 2 equations.

t=m1s+c1 and t=m2s+c2 . Then m1s+c1=m2s+c2

s= (c2-c1)/(m1-m2) , t=m1*s+c1

Use **SLOPE **and **INTERCEPT **functions to replicate these equations in excel.

s=(INTERCEPT(y-values2,x-values2)-INTERCEPT(y-values1,x-values1))/(SLOPE(y-values1,x-values1)-SLOPE(y-values2,x-values2))

t =SLOPE(y-values1,x-values1)*X+INTERCEPT(y-values1,x-values1)

For example : I take the following equations :

y1 = 2.5x1 - 0.5

y2=-0.5x1+1.67

Based on the above equations i created data for y1 and y2 using same values on X1.

**Download the excel file****STEP I: To find the intersection point :**

Apply the following formulas :

X=(INTERCEPT(y-values2,x-values2)-INTERCEPT(y-values1,x-values1))/(SLOPE(y-values1,x-values1)-SLOPE(y-values2,x-values2))

and

Y =SLOPE(y-values1,x-values1)*X+INTERCEPT(y-values1,x-values1)

**STEP II:**

Insert Scatter with Straight lines chart and mark intersection point (

**Right click on lines >> Format Data series >> Marker Options / Fill**)

Excel : Intersection of 2 linear Straight Lines |

**Click on the link below to download this file**

**Intersection between lines**

**Related link :**

**Intersection between curve and straight line**

Very good tutorial, helped a lot today! Thank you :)

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ReplyDeleteLet say i have a sinusoidal equation, y = A sin wt and a straight line equation, y = mt + c. how do i determine the intersection between those graphs?

Sorry, I am slow and got little from it. Perhaps, some practical examples would help. I have home with a roof with a 6:12 slope. I want to add a porch with a 4:12 slope. The porch (with eave) is 11.5 feet wide. How long will the rafter be from the porch's eave up the main roof to the interception point?

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