Slope intercept equation????????

Question

 

Given points A (0,3) , B (-6,2) , C (-3,6), find the slope-intercept equation of the line that passes through C and is parallel to AB.

Answer 1

The line of the points are A(0,3) and B(-6,2)

The another line is parallel to AB and passes through the point C(-3,6)

Two lines are parallel then the slopes are equal.

The slope of AB line is equal to another slope of line

A(x1,y1) and B(x2,y2) then the slope m = (y2 - y1) / (x2 - x1)

Substitute x1 =0, y1 =3, x2 =-6 and y2 =2

Slope m = (2 - 3) / (-6 - 0)

m = -1 / -6

m = 1 / 6

 Passes through the point C(-3,6) and parallel then

Point C(-3,6) and slope m = 1 / 6

Point (x1, y1) and slope m then the equation form is y - y1 = m(x - x1)

Substitute m = 1 /6, x1 = -3, y1 = 6

y - 6 = 1 / 6(x - (-3))

y - 6 = 1 / 6(x + 3)

Recall:Distributive property a(b + c) = ab + ac

y - 6= 1/6(x) + 3/6

Add 6 to each side

y - 6+ 6 = 1/6(x) +1/2 + 6

y = 1/6(x) + 13/2

The slope-intercept equation of the line : y = 1/6(x) + 13/2.

Answer 2

 

The lines are parallel so slope is same.

First find the slope of the line using any two points A (0,3) , B (-6,2)
m = (y2 - y1)/(x2-x1)
m = (2 - 3(/(-6-0) = 1/6
the slope intercept form line equation is y = mx + b. m is slope and b is y-intercept.
Find the y -intercept value by replacing the x and y values using point c(-3,6)
6 = 1/6 * -3 + b
b = 6 + 1/2 = 13/2
the line equation is y = 1/6x + 13/2