The equations are graphed in the $x y$ -plane. Which equation's graph will have a slope of $\frac{7}{8}$ and a $y$ intercept of $3$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $7 x+8 y=24$ $\newline$ (B) $7 x-8 y=-24$ $\newline$ (C) $8 x+7 y=3$ $\newline$ (D) $7 x-8 y=3$

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Algebra 1

Slope-intercept form: write an equation

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Q. The equations are graphed in the

x y

-plane. Which equation's graph will have a slope of

\frac{7}{8}

and a

y

intercept of

3

\newline

Choose

1

answer:

\newline

(A)

7 x+8 y=24

\newline

(B)

7 x-8 y=-24

\newline

(C)

8 x+7 y=3

\newline

(D)

7 x-8 y=3

Understand slope-intercept form: Understand the slope-intercept form of a linear equation. $\newline$ The slope-intercept form of a linear equation is $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept. We need to find an equation that can be rearranged into this form with a slope of $\frac{7}{8}$ and a y-intercept of $3$ .
Analyze option (A): Analyze option (A) $7x + 8y = 24$ . To put this equation into slope-intercept form, we need to solve for $y$ . $8y = -7x + 24$ $y = (-\frac{7}{8})x + 3$ This equation has a slope of $-\frac{7}{8}$ and a $y$ -intercept of $3$ , which does not match the required slope of $\frac{7}{8}$ .
Analyze option (B): Analyze option (B) $7x - 8y = -24$ . To put this equation into slope-intercept form, we need to solve for $y$ . $-8y = -7x - 24$ $y = \frac{7}{8}x + 3$ This equation has a slope of $\frac{7}{8}$ and a $y$ -intercept of $3$ , which matches the required slope and $y$ -intercept.
Analyze option (C): Analyze option (C) $8x + 7y = 3$ . To put this equation into slope-intercept form, we need to solve for $y$ . $7y = -8x + 3$ $y = (-\frac{8}{7})x + \frac{3}{7}$ This equation has a slope of $-\frac{8}{7}$ and a y-intercept of $\frac{3}{7}$ , which does not match the required slope of $\frac{7}{8}$ nor the y-intercept of $3$ .
Analyze option (D): Analyze option (D) $7x - 8y = 3$ . $\newline$ To put this equation into slope-intercept form, we need to solve for $y$ . $\newline$ $-8y = -7x + 3$ $\newline$ $y = \frac{7}{8}x - \frac{3}{8}$ $\newline$ This equation has a slope of $\frac{7}{8}$ but a y-intercept of $-\frac{3}{8}$ , which does not match the required y-intercept of $3$ .