I need help understanding functions.

Question

Give the equation of a line that goes through the point  and is parallel to the line .Write your equation in slope-intercept form.

Answer 1

Give the equation of a line that goes through the point (4,−2) and is parallel to the line 7x−4y=12.Write your equation in slope-intercept form.

The slope-intercept form of the equation of a line is:

y = mx + b

where

m = slope

the point (0,b) is the y-intercept [that is, the place where x=0]

In slope intercept form, the equation 7x-4y = 12 is:

y = (7/4)x -3

The slope is (7/4).

The parallel line has the formula: y = (7/4)x + b

Now, you may insert the (x,y) values of (4,-2) to solve for b.

-2 = (7/4)(4) + b

-2 - 7 = b

-9 = b

The equation of the parallel line (in slope-intercept form) is:

y = (7/4)x - 9

Check:

does -2 = (7/4)(4) - 9 ?

-2 = 7 - 9 ?

-2 = -2 ? yes