Writing the Equation of a Line in Slope-Intercept Form Using Two Points

The slope m and the y-intercept b of a line must be known to write a linear equation in slope-intercept form. y=mx+b When only two points on the line are known, the following four-step method can be used. For example, the equation of the line that passes through the points (- 4,1) and (8,4) will be written.

Find the Slope

Given two points on a line, the slope of the line can be found by using the Slope Formula. In this case, the coordinates ( - 4, 1) and ( 8, 4) will be substituted in place of (x_1,y_1) and (x_2,y_2), respectively.

m = y_2-y_1/x_2-x_1

SubstitutePoints

Substitute ( - 4, 1) & ( 8,4)

m=4- 1/8-( - 4)

SubNeg

a-(- b)=a+b

m=4-1/8+4

AddSubTerms

Add and subtract terms

m=3/12

CalcQuot

Calculate quotient

m=0.25

The slope m of the line passing through the two points is 0.25.

Replace m With the Slope

Now that the value of the slope is known, it can be substituted for m in the slope-intercept form of an equation. y= mx+b ⇓ y= 0.25x+b

Find b Using a Point

Next, the y-intercept can be found by substituting either of the given points into the equation and solving for b. In the considered example, (8,4) can be used. Substitute its coordinates into the equation from Step 2 and solve for b.

y=0.25x+b

SubstituteII

x= 8, y= 4

4=0.25( 8)+b

Multiply

4=2+b

SubEqn

LHS-2=RHS-2

2=b

RearrangeEqn

Rearrange equation

b=2

Therefore, the y-intercept is 2.

Write the Equation

Lastly, the complete equation in slope-intercept form can be written by substituting the y-intercept into the equation from Step 2. y=0.25x+ b ⇓ y=0.25x+ 2 The equation of the line in slope-intercept form is now complete.

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