Question

46 what is the equation of the line in the graph below? a. $y = -\frac{4}{3}x + 3$ b. $y = -\frac{4}{3}x + 4$ c. $y = -\frac{3}{4}x + 3$ d. $y = -\frac{3}{4}x + 4$ 7 which of the graphs below represents $x \geq -1$?

Explanation:

Step1: Identify two points on the line

From the graph, the line passes through \((0, 3)\) (y-intercept) and \((4, 0)\) (x-intercept).

Step2: Calculate the slope (\(m\))

Using the slope formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\), substitute \((x_1,y_1)=(0,3)\) and \((x_2,y_2)=(4,0)\):
\(m=\frac{0 - 3}{4 - 0}=\frac{-3}{4}=-\frac{3}{4}\).

Step3: Use slope - intercept form (\(y = mx + b\))

The y - intercept (\(b\)) is 3 (from the point \((0, 3)\)). Substitute \(m = -\frac{3}{4}\) and \(b = 3\) into \(y=mx + b\):
\(y=-\frac{3}{4}x + 3\).

Answer:

C. \(y = -\frac{3}{4}x + 3\)