Question

which equation is best represented by this graph?
$y = -\frac{7}{4}x + 4$
$y = -\frac{4}{7}x + 4$
$y = -\frac{4}{7}x + 7$
$y = -\frac{7}{4}x + 7$

Explanation:

Step1: Find the y - intercept

The line crosses the y - axis at the point (0, 7), so the y - intercept $b = 7$.

Step2: Find the slope

Using two points on the line, say (0,7) and (4,0). The slope $m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{0 - 7}{4-0}=-\frac{7}{4}$.

Step3: Write the equation

The slope - intercept form of a line is $y=mx + b$. Substituting $m =-\frac{7}{4}$ and $b = 7$, we get $y=-\frac{7}{4}x + 7$.

Answer:

$y =-\frac{7}{4}x + 7$