Question

which of the following graphs represents the equation $-4x + 10y = 36$?
a
b
c
d

Explanation:

Step1: Rewrite in slope-intercept form

First, solve for $y$ to get $y=mx+b$:
$$-4x + 10y = 36$$
$$10y = 4x + 36$$
$$y = \frac{4}{10}x + \frac{36}{10}$$
$$y = \frac{2}{5}x + 3.6$$

Step2: Find x-intercept (y=0)

Set $y=0$ and solve for $x$:
$$0 = \frac{2}{5}x + 3.6$$
$$\frac{2}{5}x = -3.6$$
$$x = -3.6 \times \frac{5}{2} = -9$$

Step3: Find y-intercept (x=0)

Set $x=0$ and solve for $y$:
$$y = \frac{2}{5}(0) + 3.6 = 3.6$$

Step4: Match intercepts to graphs

The line has a positive slope, y-intercept ~3.6, and x-intercept -9, which matches Graph C.

Answer:

C