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What is the rate of change, y intercept, and is it proportional for both of these equations?

y = -2x - 8
y = 15x
A) Rate of change for 1 is -2, for 2 is 15
B) Y-intercept for 1 is -8, for 2 is 0
C) Both are proportional
D) None of the above

User Jaemin
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Final answer:

The rate of change for the first equation is -2, and for the second equation, it is 15. The y-intercept for the first equation is -8, and for the second, it is 0. Only the second equation is proportional because it passes through the origin.

Step-by-step explanation:

The rate of change in a linear equation corresponds to the slope of the line, which is the coefficient of x. For the equation y = -2x - 8, the rate of change is -2, and for y = 15x, the rate of change is 15. Thus, the correct answer for the rate of change is A) Rate of change for 1 is -2, for 2 is 15.

Regarding the y-intercept, it is the constant term in the equation where the line crosses the y-axis when x is zero. For y = -2x - 8, the y-intercept is -8, and for y = 15x, the y-intercept is 0 since there is no constant term. Hence, B) Y-intercept for 1 is -8, for 2 is 0 is the correct answer for the y-intercept.

An equation is considered proportional if it passes through the origin (0,0), meaning its y-intercept is zero. The second equation, y = 15x, is proportional because it has a y-intercept of 0, but the first equation, y = -2x - 8, is not proportional because its y-intercept is -8. Therefore, the answer is C) Both are proportional is not accurate. Only the second equation is proportional.

User Raouaoul
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