Question

The Slope-Intercept equation is y = MX + b and only applies to lines. In the example, y = -2x + 7, the slope is represented by the -2 and the y-intercept (initial value) is represented by the +7. Is this line increasing or decreasing? How can you tell?

A) Increasing; the slope is negative.
B) Increasing; the slope is positive.
C) Decreasing; the slope is negative.
D) Decreasing; the slope is positive.

Answer 1

The line represented by the equation y = -2x + 7 is decreasing because it has a negative slope. The slope being negative indicates that as x increases, y decreases, resulting in a downward-sloping line.

Step-by-step explanation:

In the equation y = -2x + 7, the slope is represented by -2 and the y-intercept by 7. The slope of a line indicates its steepness and direction. Since the slope m is negative (-2), it tells us that for every increase in x by 1 unit (the run), the y value decreases by 2 units (the rise). Therefore, as we move from left to right along the line, the line descends. The y-intercept b is the point where the line crosses the y-axis, which is at y = 7 when x = 0. Thus, the correct answer is C) Decreasing; the slope is negative. This is because a negative slope indicates a line that moves downward as we look from left to right.