Question

6. Write an equation for the line that is parallel to the given line and that passes through the given point.

Answer 1

Answer:

The equation of new line is: $\mathbf{y=\frac{3}{4}x-12}$

Option H is correct.

Step-by-step explanation:

We need to write an equation for the line that is parallel to the given line $y=\frac{3}{4} x-9$ and point (-8,-18)

The equation of required line will in in form $y=mx+b$ where m is slope and b is y-intercept.

We need to find slope m and b y-intercept for new line.

Finding slope:

When two lines are parallel, they have the same slope.

The slope of given line can be found by comparing the equation $y=\frac{3}{4} x-9$ with $y=mx+b$

So, m = 3/4

The slope of new line will be: $m=\frac{3}{4}$

Finding y-intercept:

Using slope m = 3/4 and point (-8,-18) we can find y-intercept

$y=mx+b\\-18=\frac{3}{4}(-8)+b\\-18=-6+b\\b=-18+6\\b=-12$

So, y-intercept is b=-12

The equation of new line having m = 3/4 and b=-12 is:

$y=mx+b\\y=\frac{3}{4}x-12$

So, the equation of new line is: $\mathbf{y=\frac{3}{4}x-12}$

Option H is correct.