Question

what is the slope of the line $3x - 7y = 12$?
a. $\frac{3}{7}$
b. $-\frac{3}{7}$
c. $\frac{7}{3}$
d. $-\frac{7}{3}$

Explanation:

Step1: Convert to slope - intercept form

The slope - intercept form of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. We start with the equation $3x-7y = 12$.
First, we want to solve for $y$. Subtract $3x$ from both sides of the equation:
$-7y=-3x + 12$

Step2: Solve for y

Divide each term in the equation $-7y=-3x + 12$ by $-7$:
$y=\frac{-3x}{-7}+\frac{12}{-7}$
Simplify the fractions:
$y=\frac{3}{7}x-\frac{12}{7}$
In the slope - intercept form $y = mx + b$, the coefficient of $x$ (i.e., $m$) is the slope. Here, $m=\frac{3}{7}$.

Answer:

A. $\frac{3}{7}$