Question

Find the equation for the line parallel to y=x+3 which has the same y intercept as 2x+3y=12

Answer 1

Answer:

$y=x+4$

Step-by-step explanation:

Two parallel lines will have the same slope:

$y=mx+b$

This is the y-intercept equation, where m is the slope and b is the y-intercept:

$y=x+3$

The slope is x, or 1x, so the parallel line is also x.

Find the y-intercept:

You do this by taking the equation given and solving for y:

$2x+3y=12$

Isolate the variable y. Subtract 2x from both sides:

$2x-2x+3y=12-2x\\\\3y=12-2x$

Isolate y by dividing both sides by 3:

$\frac{3y}{3}=\frac{12}{3}-\frac{2x}{3} \\\\y=4-\frac{2}{3}x$

Rearrange in slope-intercept form:

$y=-\frac{2}{3}x+ 4$

The y-intercept of this equation is 4.

Now make the equation using the given information:

$y=x+4$

:Done