Answer:
D. <em>y</em> = (⁴/₃)<em>x</em> – 1
Step-by-step explanation:
To find the answer to this problem, we need to find the <em>slope</em> of 4<em>x</em> – 3<em>y</em> = 15 . Why? A line that is <em>parallel</em> to another line has the same slope as the other line.
The question gives the line in <em>standard form</em>, but all the options are in <em>slope-intercept form</em>. In addition, <em>standard form</em> is the only type of linear equation that does not explicitly give the slope. The slope is the change in the dependent variable, <em>y</em>, over the change in the independent variable, <em>x</em>. This means we need to solve the equation for <em>y</em> and so:
4<em>x</em> – 3<em>y</em> = 15 — original equation
4<em>x</em> – 3<em>y – </em>4<em>x</em> = 15 – 4<em>x</em> — subtracting 4<em>x</em> on each side to isolate 3<em>y</em> and reverse the addition of 4<em>x</em>
–3<em>y</em> = 15 – 4<em>x</em> — simplifying; the 4<em>x</em> on the left cancels out
–3<em>y</em> ÷ –3 = (15 – 4<em>x</em>) ÷ –3 — dividing both sides by –3 to isolate <em>y</em>
–3<em>y</em> ÷ –3 = (15 ÷ –3) + (–4<em>x</em> ÷ –3) — distributing the division by –3 on the right side to make it easier to understand
<em>y</em> = (⁴/₃)<em>x</em> – 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, <em>y</em> = (⁴/₃)<em>x</em> – 1, so that's our answer.
Of course, you could have just found two points on the graph and then used <em>point-slope form</em> to solve for the slope, but that takes more time…
I hope this makes it easier to understand the concept! Have a great day!
