Question

question 13 (1 point)
match the equation with its graph.
$7x + 5y = 35$
\\(\circ\\) a
graph a
\\(\circ\\) b
graph b
\\(\circ\\) c
graph c
\\(\circ\\) d
graph d

Explanation:

Step1: Rewrite equation in slope - intercept form

We start with the equation \(7x + 5y=35\). We want to solve for \(y\) to get it in the form \(y = mx + b\) (where \(m\) is the slope and \(b\) is the \(y\) - intercept).
Subtract \(7x\) from both sides: \(5y=-7x + 35\).
Then divide each term by 5: \(y=-\frac{7}{5}x + 7\).
So the slope \(m =-\frac{7}{5}\) (negative slope, so the line should be decreasing from left to right) and the \(y\) - intercept \(b = 7\) (the line crosses the \(y\) - axis at \((0,7)\)).

Step2: Analyze the graphs

• For graph a: The line has a positive slope (increasing from left to right) and a negative \(y\) - intercept, so it does not match.
• For graph b: The line has a positive slope (increasing from left to right) and a positive \(y\) - intercept, but the slope is not \(-\frac{7}{5}\), so it does not match.
• For graph c: The line has a negative slope (decreasing from left to right) but the \(y\) - intercept is negative, so it does not match.
• For graph d: The line has a negative slope (since \(m =-\frac{7}{5}<0\)) and the \(y\) - intercept is \(7\) (it crosses the \(y\) - axis at \((0,7)\)), which matches our equation \(y =-\frac{7}{5}x + 7\).

Answer:

d