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Function A is a linear function. An equation for Function A is $3x + 4y = 28$ . $\newline$ Which of the following functions has the same slope as Function A? $\newline$ Choices: $\newline$ (A) $y = -\frac{3}{4}x + \frac{4}{3}$ $\newline$ (B) $y = \frac{3}{4}x - \frac{4}{3}$ $\newline$ (C) $y = \frac{4}{3}x - \frac{3}{4}$ $\newline$ (D) $y = -\frac{4}{3}x + \frac{3}{4}$

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Write equations of cosine functions using properties

Full solution

Q. Function A is a linear function. An equation for Function A is

3x + 4y = 28

.

\newline

Which of the following functions has the same slope as Function A?

\newline

Choices:

\newline

(A)

y = -\frac{3}{4}x + \frac{4}{3}

\newline

(B)

y = \frac{3}{4}x - \frac{4}{3}

\newline

(C)

y = \frac{4}{3}x - \frac{3}{4}

\newline

(D)

y = -\frac{4}{3}x + \frac{3}{4}

Rewrite equation in slope-intercept form: First, we need to find the slope of Function A by rewriting the equation in slope-intercept form $y = mx + b$ , where $m$ is the slope. So, we solve for $y$ in $3x + 4y = 28$ .
Isolate y-term: Subtract $3x$ from both sides to isolate the y-term: $4y = -3x + 28$ .
Solve for y: Divide everything by $4$ to solve for y: $y = \frac{-3}{4}x + 7$ .
Identify slope of Function A: Now we know the slope of Function A is $-\frac{3}{4}$ . We need to find which of the given choices has the same slope.
Compare slopes with choices: Looking at the choices, we see that (A) $y = -\frac{3}{4}x + \frac{4}{3}$ has the same slope as Function A, which is $-\frac{3}{4}$ .

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