A line passes through the points $$ (5,-7.5) $$ and has a $$ y $$-intercept 10 . Which line has a rate of change that is less than this line's rate of change? (A) $$ y=0.5 x+10 $$ (B) $$ y=-1.5 x+10 $$ (C) $$ y=-3.5 x+10 $$ (D) $$ y=-10 x+10 $$

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To determine the rate of change of the given line, we first note that it passes through the points $$ (0, 10) $$ (the $$y$$-intercept) and $$ (5,-7.5) $$.

The slope $$ m $$ is given by

$$
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-7.5 - 10}{5 - 0} = \frac{-17.5}{5} = -3.5.
$$

This means the rate of change of the given line is $$-3.5$$.

A rate of change that is less than $$-3.5$$ must be more negative than $$-3.5$$. Let’s compare the slopes from the options:

- (A) $$ y = 0.5x + 10 $$ — slope $$ = 0.5 $$
- (B) $$ y = -1.5x + 10 $$ — slope $$ = -1.5 $$
- (C) $$ y = -3.5x + 10 $$ — slope $$ = -3.5 $$
- (D) $$ y = -10x + 10 $$ — slope $$ = -10 $$

Since $$-10 < -3.5$$, option (D) has a rate of change less than that of the given line.

Thus, the answer is

(D) $$ y = -10x + 10 $$.
The line with a slope of $$-10$$ has a rate of change less than the given line's rate of change. So, the answer is (D) $$ y = -10x + 10 $$.

A line passes through the points and has a -intercept 10 .
Which line has a rate of change that is less than this line’s rate of change?
(A)
(B)
©
(D)

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A line passes through the points and has a -intercept 10 . Which line has a rate of change that is less than this line’s rate of change? (A) (B) © (D)