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

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Grade 8

Write a linear equation from a slope and y-intercept

Full solution

Q. The equations are graphed in the

\newline

xy

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

\newline

\frac{7}{8}

and a

\newline

y

-intercept of

3

\newline

Choose

1

answer:

\newline

(A)

7x+8y=24

\newline

(B)

7x-8y=-24

\newline

(C)

8x+7y=3

\newline

(D)

7x-8y=3

Understand slope-intercept form: Understand the slope-intercept form of a line. The slope-intercept form of a line is given by $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept.
Identify slope and y-intercept: Identify the slope and y-intercept from the question prompt. $\newline$ The slope $m$ is $\frac{7}{8}$ , and the y-intercept $b$ is $3$ .
Convert equations to slope-intercept form: Convert the given equations to slope-intercept form to compare with the desired slope and $y$ -intercept. $\newline$ We need to isolate $y$ on one side of the equation for each option to compare the slopes and $y$ -intercepts.
Convert option (A): Convert option (A) $7x + 8y = 24$ to slope-intercept form. $\newline$ Subtract $7x$ from both sides to get $8y = -7x + 24$ . $\newline$ Then divide by $8$ to get $y = \left(-\frac{7}{8}\right)x + 3$ .
Check option (A): Check if option (A) matches the desired slope and y-intercept. $\newline$ The slope from option (A) is $-\frac{7}{8}$ , which does not match the desired slope of $\frac{7}{8}$ . The y-intercept is $3$ , which does match the desired y-intercept.
Convert option (B): Convert option (B) $7x - 8y = -24$ to slope-intercept form. $\newline$ Add $7x$ to both sides to get $-8y = -7x - 24$ . $\newline$ Then divide by $-8$ to get $y = \left(\frac{7}{8}\right)x + 3$ .
Check option (B): Check if option (B) matches the desired slope and y-intercept. $\newline$ The slope from option (B) is $\frac{7}{8}$ , which matches the desired slope. The y-intercept is also $3$ , which matches the desired y-intercept.
Final decision: Since option (B) matches both the slope and $y$ -intercept, there is no need to check options (C) and (D).