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

Question

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

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Understanding slope-intercept form: Understand the slope-intercept form of a linear equation. The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept. We are looking for an equation with a slope of 7/8 and a y-intercept of 3.Converting equation (A) to slope-intercept form: Convert the given equations to slope-intercept form to identify the slope and y-intercept. We will start with option (A) 7x + 8y = 24 and rearrange it to solve for y. Subtract 7x from both sides to get 8y = -7x + 24. Then divide by 8 to isolate y, yielding y = (-7/8)x + 3.Checking slope and y-intercept for equation (A): Check if the slope and y-intercept from Step 2 match the required values. The slope from equation (A) is -7/8, and the y-intercept is 3. The slope does not match the required slope of 7/8, so option (A) is not the correct answer.Converting equation (B) to slope-intercept form: Repeat Step 2 for option (B) 7x - 8y = -24. Subtract 7x from both sides to get -8y = -7x - 24. Then divide by -8 to isolate y, yielding y = (7/8)x + 3.Checking slope and y-intercept for equation (B): Check if the slope and y-intercept from Step 4 match the required values. The slope from equation (B) is 7/8, and the y-intercept is 3. Both the slope and y-intercept match the required values, so option (B) is the correct answer.

The equations are graphed in the $xy$ -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) $7x+8y=24$ $\newline$ (B) $7x-8y=-24$ $\newline$ (C) $8x+7y=3$ $\newline$ (D) $7x-8y=3$

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