Writing The Equation of a Line Given a Point and Slope

Writing The Equation of a Line Given a Point And a Slope

by Lucy Kollmann and A'dreah Hill

Introducing Point-Slope Form

If you are given the slope of a line, m, and the coordinates of one point, you can write the equation of a line. Using the point-slope form of an equation y-y₁=m(x-x₁), substituting the given data and solving for y will put an equation in slope-intercept form.

Multiple Choice

What is the point-slope formula?

• x-x₁=m(y-y₁)

• y=mx+b

• a²+b²=c²

• y-y₁=m(x-x₁)

​Example of Point-Slope Form

​Step 1: Substitute the given data into the formula y-y₁=m(x-x₁).

Step 2: Distribute the four-thirds with the values in the parentheses.

Step 3: Solve for Y.

NOTE: your answer should ALWAYS end up being in slope-intercept form.

Multiple Choice

(3,4), m = (1/2)

• y= (1/3)x - (9/2)

• y= (1/2)x - (11/2)

• x= (1/3)y- (9/2)

• y=(1/3)x - (11/2)

Multiple Choice

(-1,5), m= (2/5)

• y=(2/5)x+(17/3)

• y-(17/3)=(2/5)

• y=(1/5)+(17/3)

• y-(17/3)=(1/5)

​Another Example:

Multiple Choice

(-2,-3), m= (-3/4)

• y=(4/3)x+(8/1)

• y=(4/-3)x-(8/1)

• y=(-3/2)x-(9/2)

• y= (-3/4)x-(9/2)

Multiple Choice

(-2,1), m= (4/3)

• y=(3/4)x+(3/4)

• y=(4/3)x+(4/3)

• I don't know

• y=(3/3)x+(4/3)

Multiple Choice

(-2,5), m=(1/3)

• y=(3/2)x+(3/18)

• y=(2/3)x+(18/3)

• y=(3/1)x+(3/17)

• y=(1/3)x+(17/3)

Multiple Choice

(2,-4), m=1

• y=x-6

• y+6=x

• x=7+y

• y=x-7