## Algebra 1: Common Core (15th Edition)

The x-intercept is $\frac{1}{3}$. The y-intercept is $1$.
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 $1$.