Answer:
the second option: [tex]7x+4y=44[/tex]
Step-by-step explanation:
So when a line is parallel, it means that it has the same slope and a different y-intercept, it's important that there is a different y-intercept, otherwise it would be the same line, and the "two lines" would intersect at infinite points.
Anyways by looking at the graph you have two points (-8, 5) and (-4, -2). So the run in this case was 4 and the rise was -7. This is a slope of -7/4. So we have the equation: [tex]y=-\frac{7}{4}x+b \text{ where b}\ne-9}[/tex]. Since it passes through the point (8, -3) we can plug that in as (x, y) to solve for b (the y-intercept)
Plug in (8, -3) as (x, y)
[tex]-3=-\frac{7}{4}(8)+b[/tex]
Multiply the -7/4 and 8
[tex]-3 = -14+b[/tex]
add 4 to both sides
[tex]11 = b[/tex]
So this gives us the equation:
[tex]y=-\frac{7}{4}x+11[/tex]
Since it's asking for it in standard form you move the 7/4 x to the other side
Add 7/4x to both sides
[tex]\frac{7}{4}x+y=11[/tex]
Multiply both sides by 4 to cancel out the fraction
[tex]7x+4y=44[/tex]
