Question

The equation of line AB is y = 2x + 4. Write an equation of a line parallel to line AB in slope-intercept form that contains point (3, −2). (4 points) y = 2x + 4 y = negative 1 over 2 x − 1 over 2 y = − 1 over 2 x − 7 over 2 y = 2x − 8

Answer 1

ANSWER

$y = 2x - 8$

EXPLANATION

To find the equation of a straight line, we need the slope and a point on that line.

We were given the equation of another line that will help us determine the slope . The given line has equation:

$y = 2x + 4$

This equation is of the form

$y = mx + b$

where

$m = 2 \: \: is \: the \: \: slope.$

Since our line of interest is parallel to this line, their slopes are the same.

The line also contains the point (3,-2).

So we substitute the slope and point into the slope-intercept formula:

$- 2= 2(3)+ b$

$- 2 =6 + b$

$\implies \: b = - 2 - 6 = - 8$

The required equation is

$y = 2x - 8$