Question

select the graph of $y = -3x + 5$.

a) graph with a line, axes, origin o

b) graph with a line, axes, origin o

c) graph with a line, axes, origin o

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 \(y=-3x + 5\), the slope \(m=-3\) (negative, so the line should be decreasing from left to right) and the y - intercept \(b = 5\) (the line crosses the y - axis at \(y = 5\)).

Step2: Analyze each option

• Option A: The line has a positive slope (increasing from left to right) and a positive y - intercept. But our slope is negative, so A is incorrect.
• Option B: The line has a positive slope (increasing from left to right) and a negative y - intercept. Our slope is negative and y - intercept is positive, so B is incorrect.
• Option C: The line has a negative slope (decreasing from left to right) and we can check the y - intercept. When \(x = 0\), \(y=5\) (positive y - intercept), which matches our equation.

Answer:

C (The graph in option C)