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What is the rate of change in the equation [tex]\( y = -\frac{7}{8}x - 5 \)[/tex]?

A. 1
B. 5
C. [tex]\(-5\)[/tex]
D. [tex]\(-\frac{7}{8}\)[/tex]
E. [tex]\(-\frac{70}{8}\)[/tex]

Answer :

To find the rate of change, we first rewrite the given equation into slope-intercept form, which is:

[tex]$$
y = mx + b.
$$[/tex]

The original equation is:

[tex]$$
-5 - \frac{7}{8}x = y.
$$[/tex]

We can rearrange it to match the slope-intercept format:

[tex]$$
y = -\frac{7}{8}x - 5.
$$[/tex]

In this form, the coefficient of [tex]$x$[/tex] represents the rate of change (or slope), so we have:

[tex]$$
m = -\frac{7}{8}.
$$[/tex]

Thus, the rate of change in the equation is:

[tex]$$
-\frac{7}{8}.
$$[/tex]

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