Question

multiple choice 10 points what is the equation of the line with an x-intercept of 3 and a y-intercept of -4? \\( y = \frac{3}{4}x - 4 \\) \\( y = \frac{4}{3}x - 4 \\) \\( y = -4x + 3 \\) \\( y = -\frac{4}{3}x - 4 \\)

Explanation:

Step1: Recall intercept form of line

The intercept form of a line is $\frac{x}{a}+\frac{y}{b} = 1$, where $a$ is the x - intercept and $b$ is the y - intercept. Here, $a = 3$ and $b=-4$.
So, $\frac{x}{3}+\frac{y}{-4}=1$.

Step2: Convert to slope - intercept form

First, rewrite the equation: $\frac{x}{3}-\frac{y}{4}=1$.
Multiply through by 12 to clear the fractions: $4x - 3y=12$.
Then, solve for $y$:
$-3y=-4x + 12$
$y=\frac{4}{3}x-4$

Answer:

$y = \frac{4}{3}x-4$ (the second option)