Question

what is the equation of the graphed line written in standard form?
3x + y = -5
x + 3y = -5
3x - 5y = -15
5x - 3y = 15

Explanation:

Step1: Identify two points on the line

From the graph, the line passes through \((0, -5)\) (y-intercept) and \((3, 0)\) (x-intercept).

Step2: Calculate the slope \(m\)

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Using \((0, -5)\) as \((x_1,y_1)\) and \((3, 0)\) as \((x_2,y_2)\), we get \(m=\frac{0 - (-5)}{3 - 0}=\frac{5}{3}\).

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

We know \(m=\frac{5}{3}\) and \(b=-5\) (from the y - intercept \((0, - 5)\)), so the equation is \(y=\frac{5}{3}x-5\).

Step4: Convert to standard form \(Ax + By = C\)

Multiply every term by 3 to eliminate the fraction: \(3y = 5x-15\). Rearrange to get \(5x-3y = 15\).

Answer:

D. \(5x - 3y = 15\)