Answer
The x-intercept is $4$. The y-intercept is $\frac{-8}{5}$
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:
$m=\frac{-2-0.4}{-1-5}=\frac{2}{5}$
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:
$y-(-2)=\frac{2}{5}(x-(-1))$
$y+2=\frac{2}{5}(x+1)$
This is the point-slope formula of the equation.
To find the x-intercept, we set y equal to 0:
$0+2=\frac{2}{5}(x+1)$
Use the distributive property on the right side of the equation:
$\frac{2}{5}x+\frac{2}{5}=2$
$x=4$
To find the y-intercept, we set x equal to 0:
$y+2=\frac{2}{5}(0+1)$
$y+2=\frac{2}{5}$
$y=\frac{-8}{5}$
The x-intercept is $4$. The y-intercept is $\frac{-8}{5}$.
