Answer:
The equation of new line is: [tex]\mathbf{y=\frac{3}{4}x-12}[/tex]
Option H is correct.
Step-by-step explanation:
We need to write an equation for the line that is parallel to the given line [tex]y=\frac{3}{4} x-9[/tex] and point (-8,-18)
The equation of required line will in in form [tex]y=mx+b[/tex] 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 [tex]y=\frac{3}{4} x-9[/tex] with [tex]y=mx+b[/tex]
So, m = 3/4
The slope of new line will be: [tex]m=\frac{3}{4}[/tex]
Finding y-intercept:
Using slope m = 3/4 and point (-8,-18) we can find y-intercept
[tex]y=mx+b\\-18=\frac{3}{4}(-8)+b\\-18=-6+b\\b=-18+6\\b=-12[/tex]
So, y-intercept is b=-12
The equation of new line having m = 3/4 and b=-12 is:
[tex]y=mx+b\\y=\frac{3}{4}x-12[/tex]
So, the equation of new line is: [tex]\mathbf{y=\frac{3}{4}x-12}[/tex]
Option H is correct.
