Question

find an equation of the line graphed. write the equation in standard form. choose the correct equation below. a. $4x + 3y = -16$ b. $4x - 3y = -16$ c. $3x + 4y = -16$ d. $3x - 4y = -16$

Explanation:

Step1: Identify two points

From the graph, two points on the line are \((-4, 1)\) and \((4, 7)\) (or other visible points, e.g., y-intercept \((0, 4)\) and \((-4, 1)\)). Let's use \((-4, 1)\) and \((4, 7)\).

Step2: Calculate the slope

Slope \(m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{7 - 1}{4 - (-4)} = \frac{6}{8} = \frac{3}{4}\).

Step3: Use point - slope form

Using point \((0, 4)\) (y - intercept), the slope - intercept form is \(y = mx + b\), so \(y=\frac{3}{4}x + 4\).

Step4: Convert to standard form

Multiply both sides by 4 to eliminate fraction: \(4y = 3x+16\). Rearrange to \(3x - 4y=- 16\) (standard form \(Ax + By = C\), \(A\geq0\)).

Answer:

D. \(3x - 4y=-16\)