Question

question 7
review chapter 4 test - algebra
select the graph of $y = -3x + 5$.
a) graph of a line with positive slope, y-intercept positive
b) graph of a line with positive slope, y-intercept negative
c) graph of a line with negative slope, y-intercept near zero

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: Evaluate each option

• Option A: The line has a positive slope (increasing from left to right), which does not match \(m=-3\). So A is incorrect.
• Option B: The line has a positive slope and a negative y - intercept, which does not match our equation. So B is incorrect.
• Option C: The line has a negative slope (decreasing from left to right) and we can infer from the graph that it has a positive y - intercept (consistent with \(b = 5\) in terms of the sign of the y - intercept and the slope sign). So C matches the equation \(y=-3x + 5\).

Answer:

C) (the graph with the line decreasing from left to right and crossing the y - axis above the origin)