Answer
The x-intercept is $\frac{1}{3}$. The y-intercept is $1$.
Work Step by Step
To find the x-intercept and y-intercept of the line, we first need to find the equation of the line.
We can use the two points given to formulate the point-slope form.
Let's first find the slope:
$m = \frac{y_2 - y_1}{x_2 - x_1}$, where $m$ is the slope and $(x_1, y_1)$ and $(x_2, y_2)$ are points on the line.
Let's plug in our two points into this formula:
$m = \frac{13 - (-8)}{-4 - 3}$
Simplify by adding or subtracting in the numerator and denominator:
$m = \frac{21}{-7}$
Divide both the numerator and denominator by their greatest common factor, $7$:
$m = -3$
Since we have the slope and two points, we can use the point-slope form, which is given by the following formula:
$y - y_1 = m(x - x_1)$
Let's plug in the slope and a point into this formula:
$y - (-8) = -3(x - 3)$
Simplify the left side of the equation:
$y + 8 = -3(x - 3)$
This is the point-slope formula of the equation.
To find the x-intercept, we set $y$ equal to $0$:
$0 + 8 = -3(x - 3)$
Use the distributive property on the right side of the equation:
$8 = -3x + 9$
Subtract $8$ from both sides of the equation to move constants to one side of the equation:
$0 = -3x + 1$
Add $3x$ to both sides of the equation:
$3x = 1$
Divide both sides of the equation by $3$ to solve for $x$:
$x = \frac{1}{3}$
To find the y-intercept, we set $x$ equal to $0$:
$y + 8 = -3(0 - 3)$
Evaluate what's in parentheses first:
$y + 8 = -3(-3)$
Simplify the right side of the equation:
$y + 8 = 9$
Subtract $8$ from both sides of the equation to solve for $y$:
$y = 1$
The x-intercept is $\frac{1}{3}$. The y-intercept is $1$.
