Question

Given the following equation check all that apply. y ≤ 5x -7

a) The slope of the line is 5
b) The y-intercept is -7
c) The solution set includes points below the line
d) The solution set includes points on the line

Answer 1

The given equation y ≤ 5x - 7 has a slope of 5, a y-intercept of -7, and includes points both below and on the line.

Step-by-step explanation:

The given equation is y ≤ 5x - 7. Let's analyze each option:

1. a) The slope of the line is 5. The slope is the coefficient of x, which is 5 in this case. So, a) is correct.
2. b) The y-intercept is -7. The y-intercept is the value of y when x = 0. In this equation, the y-intercept is -7. So, b) is correct.
3. c) The solution set includes points below the line. Since the inequality sign is ≤, the points on or below the line are included in the solution set. So, c) is correct.
4. d) The solution set includes points on the line. Since the inequality sign is ≤, the points on the line itself are included in the solution set. So, d) is correct.

Therefore, options a), b), c), and d) are all correct.