Question

determine the intercepts of the line. do not round your answers. y - 3 = 5(x - 2) y - intercept: ( , ) x - intercept: ( , ) related content intercepts from an equation

Explanation:

Step1: Find y - intercept

Set \(x = 0\) in the equation \(y-3 = 5(x - 2)\).
\[

$$\begin{align*} y-3&=5(0 - 2)\\ y-3&=5\times(- 2)\\ y-3&=-10\\ y&=-10 + 3\\ y&=-7 \end{align*}$$

\]
So the y - intercept is \((0,-7)\).

Step2: Find x - intercept

Set \(y = 0\) in the equation \(y-3 = 5(x - 2)\).
\[

$$\begin{align*} 0-3&=5(x - 2)\\ -3&=5x-10\\ 5x&=-3 + 10\\ 5x&=7\\ x&=\frac{7}{5}=1.4 \end{align*}$$

\]
So the x - intercept is \((1.4,0)\).

Answer:

y - intercept: \((0,-7)\)
x - intercept: \((1.4,0)\)