Question

use a graphing utility to graph the equation. use a standard setting. approximate any intercepts of the graph. (if an answer does not exist, enter dne.)
y = |x + 5|
x-intercept (x, y) = (□)
y-intercept (x, y) = (□)

Explanation:

Step1: Find x-intercept (set \( y = 0 \))

To find the x - intercept, we set \( y = 0 \) in the equation \( y=\vert x + 5\vert \). So we have the equation \( 0=\vert x + 5\vert \). The absolute value of a number is zero when the number inside the absolute value is zero. So \( x+5 = 0 \), which gives \( x=- 5 \). So the x - intercept is \( (-5,0) \).

Step2: Find y-intercept (set \( x = 0 \))

To find the y - intercept, we set \( x = 0 \) in the equation \( y=\vert x + 5\vert \). Substitute \( x = 0 \) into the equation: \( y=\vert0 + 5\vert=\vert5\vert = 5 \). So the y - intercept is \( (0,5) \).

Answer:

x - intercept \((x,y)=(-5,0)\)
y - intercept \((x,y)=(0,5)\)