Question

which graph shows $y = -3x + 2$?
a
b
c
d
select your answer choice below.
which table contains only values that satisfy the equation $y = 0.5x + 14$?

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 \(y=-3x + 2\), the slope \(m=-3\) (negative, so the line should be decreasing from left to right) and the y - intercept \(b = 2\) (the line crosses the y - axis at \((0,2)\)).

Step2: Analyze each option

• Option A: The line has a positive slope (increasing from left to right), so it does not match the slope of \(-3\). Eliminate A.
• Option B: The y - intercept of the line in this graph does not appear to be \(2\) (it looks like it crosses the y - axis at a negative value or a value far from \(2\)). Eliminate B.
• Option C: The line has a positive slope (increasing from left to right), so it does not match the slope of \(-3\). Eliminate C.
• Option D: The line has a negative slope (decreasing from left to right) and the y - intercept appears to be \(2\) (crosses the y - axis near \((0,2)\)). Also, the steepness of the line is consistent with a slope of \(-3\) (for every \(1\) unit increase in \(x\), \(y\) decreases by \(3\) units).

Answer:

D