Answer
x-intercept = $-2$
y-intercept = $-2$
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:
$m = \frac{-5 - 4}{3 - (-6)}$
Simplify by adding or subtracting in the numerator and denominator:
$m = \frac{-9}{9}$
Simplify by dividing both the numerator and denominator by their greatest common factor, $9$:
$m = -1$
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:
$y - 4 = -1(x - (-6))$
Simplify the right side of the equation:
$y - 4 = -1(x + 6)$
Use the distributive property on the right side of the equation:
$y - 4 = -x - 6$
This would be the point-slope form of the equation, but we want the slope-intercept form, so we need to isolate $y$ on the left side of the equation by adding $4$ to both sides of the equation:
$y = -x - 2$
To find the x-intercept, we set $y$ equal to $0$:
$0 = -x - 2$
Add $x$ to each side of the equation to move the variable to the left side of the equation:
$x = -2$
To find the y-intercept, we set $x$ equal to $0$:
$y = -(0) - 2$
Subtract to solve:
$y = -2$
The x-intercept is $-2$. The y-intercept is $-2$.
