Question

which graph represents $y = -\frac{3}{2}x + 4$ ?

Explanation:

Step1: Analyze the slope and y-intercept

The equation is in slope - intercept form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. For the equation \(y=-\frac{3}{2}x + 4\), the slope \(m =-\frac{3}{2}\) (negative, so the line should be decreasing from left to right) and the y - intercept \(b = 4\) (the line crosses the y - axis at \((0,4)\)).

Step2: Analyze each graph

• First graph: The line is increasing (positive slope), so it can't be this one.
• Second graph: The line is increasing (positive slope), so it can't be this one.
• Third graph: The y - intercept is at a negative value (not 4), so it can't be this one.
• Fourth graph: The line is decreasing (negative slope) and the y - intercept appears to be at \((0,4)\) (since when \(x = 0\), \(y=4\)) and the slope of \(-\frac{3}{2}\) (for every 2 units we move to the right, we move down 3 units) is consistent with the points on the line.

Answer:

The Right Graph (the fourth graph from the left)