Question

which of the following could be the equation of the graph shown below? check all that apply. a. -4x + 2y = -6 b. 2x - 3y = -9 c. y = -10 d. y = 3x - 2

Explanation:

Step1: Analyze the graph's slope and y-intercept

The graph is a straight line with a positive slope (rising from left to right) and a negative y - intercept (crosses the y - axis below the origin). Let's convert each equation to slope - intercept form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept.

Step2: Analyze Option A

For the equation \(-4x + 2y=-6\), solve for \(y\):
Add \(4x\) to both sides: \(2y = 4x-6\)
Divide by 2: \(y = 2x - 3\)
Slope \(m = 2\) (positive), y - intercept \(b=-3\) (negative). This is a possible equation.

Step3: Analyze Option B

For the equation \(2x-3y=-9\), solve for \(y\):
Subtract \(2x\) from both sides: \(-3y=-2x - 9\)
Divide by \(-3\): \(y=\frac{2}{3}x + 3\)
Slope \(m=\frac{2}{3}\) (positive), but y - intercept \(b = 3\) (positive). This does not match the graph.

Step4: Analyze Option C

The equation \(y=-10\) is a horizontal line (slope \(m = 0\)) with y - intercept \(b=-10\). The graph is not horizontal, so this is not a possible equation.

Step5: Analyze Option D

The equation \(y = 3x-2\) is in slope - intercept form. Slope \(m = 3\) (positive), y - intercept \(b=-2\) (negative). This is a possible equation.

Answer:

A. \(-4x + 2y=-6\), D. \(y = 3x-2\)