Answer
The x-intercept is $6$. The y-intercept is $6$.
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:
$m = \frac{2 - 8}{4 - (-2)}$
Simplify by adding or subtracting in the numerator and denominator:
$m = \frac{-6}{6}$
Divide both the numerator and denominator by their greatest common factor, $6$:
$m = -1$
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:
$y - 2 = -1(x - 4)$
Simplify the right side of the equation:
$y - 2 = -x + 4$
This is the point-slope formula of the equation.
To find the x-intercept, we set $y$ equal to $0$:
$0 - 2 = -x + 4$
Add $2$ to both sides of the equation to move constants to one side of the equation:
$0 = -x + 6$
Add $x$ to both sides of the equation:
$x = 6$
To find the y-intercept, we set $x$ equal to $0$:
$y - 2 = -0 + 4$
Add $2$ to each side of the equation:
$y = 6$
The x-intercept is $6$. The y-intercept is $6$.
