О с. А о. Sign
Which of the following lines is parallel to the
line 4x - 3y = 15?
A. y=4x-5

B. y=-3/4x+2

C. y=3/4x+8

D. y=4/3x-1

Step-by-step explanation:

To be parallel the slopes must be equal

4x-3y=15

3y=4x-15

y=(4x-15)/3

so m=4/3

Only line D. has a slope of 4/3

D. y = (⁴/₃)x – 1

Step-by-step explanation:

To find the answer to this problem, we need to find the slope of 4x – 3y = 15 . Why? A line that is parallel to another line has the same slope as the other line.

The question gives the line in standard form, but all the options are in slope-intercept form. In addition, standard form is the only type of linear equation that does not explicitly give the slope. The slope is the change in the dependent variable, y, over the change in the independent variable, x. This means we need to solve the equation for y and so:

4x – 3y = 15  — original equation

4x – 3y – 4x = 15 – 4x  — subtracting 4x on each side to isolate 3y and reverse the addition of 4x

–3y = 15 – 4x  — simplifying; the 4x on the left cancels out

–3y ÷ –3 = (15 – 4x) ÷ –3  — dividing both sides by –3 to isolate y

–3y ÷ –3 = (15 ÷ –3) + (–4x ÷ –3)  — distributing the division by –3 on the right side to make it easier to understand

y = (⁴/₃)x – 5  — simplifying; this is our expression for y, and it gives us the slope

Now, which line has a slope of ⁴/₃? That would be Option D, y = (⁴/₃)x – 1, so that's our answer.

Of course, you could have just found two points on the graph and then used point-slope form to solve for the slope, but that takes more time…

I hope this makes it easier to understand the concept! Have a great day!