Question

Write an equation in the form y = mx + b of the line that is described. The line has the same y-intercept as the line whose equation is y = - 2 + x and is

parallel to the line whose equation is 3x + 3y = 6.

Answer 1

y=x+2

Explanation:

So, our line has the same y intercept as the equation is y=-2+x, and parallel to 3x+3y=6

We want to write the equation in y=mx+b form, where m is the slope and b is the y intercept

The y intercept of y=-2+x is -2, (we can rearrange it to be y=x-2) so that's the y intercept of our line

so far, here's our line:

y=mx-2

First, let's put 3x+3y=6 into slope-intercept form

subtract 3x from both sides

3y=-3x+6

divide by 3

y=-x+2

Perpendicular lines are negative and reciprocal; if you multiply their slopes together, the result is -1.

The slope for y=-x+2 is -1.

To find the slope of the new line:

-1m=-1

divide by -1

m=1

The slope of our line is 1

here's our line:

y=x+2

hope this helps!