Answer
The x-intercept is $\frac{-53}{5}$
The y-intercept is $\frac{53}{3}$
Work Step by Step
To find the x-intercept and the 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:
$m=\frac{11-6}{-4-(-7)}=\frac{5}{3}$
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:
$y-11=\frac{5}{3}(x-(-4))$
$y-11=\frac{5}{3}(x+4)$
This is the point-slope formula of the equation.
To find the x-intercept, we set y equal to 0:
$0-11=\frac{5}{3}(x+4)$
Use the distributive property on the right side of the equation:
$\frac{5}{3}x+\frac{20}{3}=-11$
$x=\frac{-53}{5}$
To find the y-intercept, we set x equal to 0:
$y-11=\frac{5}{3}(0+4)$
$y-11=\frac{20}{3}$
$y=\frac{53}{3}$
The x-intercept is $\frac{-53}{5}$. The y-intercept is $\frac{53}{3}$.
