Find an equation of the line that satisfies the conditions. Write the equation in standard form.
-Through $(0,5) ; m=\frac{3}{4}$
A) $3 x+4 y=-20$
B) $4 x-3 y=-20$
C) $3 x-4 y=20$
D) $3 x-4 y=-20$

Question

Quizplus · Accepted Answer

The equation of a line in slope-intercept form is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. Given $m = \frac{3}{4}$ and it passes through $(0,5)$, we substitute these values to find $b$: $5 = \frac{3}{4}(0) + b$, so $b = 5$. The equation becomes $y = \frac{3}{4}x + 5$. To convert to standard form $Ax + By = C$, we multiply everything by 4 to clear the fraction: $4y = 3x + 20$, then rearrange to $3x - 4y = -20$, which matches option D.

Find an Equation of the Line That Satisfies the Conditions (0,5);m=34(0,5) ; m=\frac{3}{4}(0,5);m=43​

Find an Equation of the Line That Satisfies the Conditions $(0,5) ; m=\frac{3}{4}$