Question

find the x- and y-intercepts.
\\( y = |x - 7| - 3 \\)
write each intercept as an ordered pair.
if there is more than one intercept, use the \and\ button.
select
one\ if applicable.
part 1 of 2
x-intercept(s):

Explanation:

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

Set $y=0$, so $0 = |x-7| - 3$

Step2: Isolate the absolute value

Rearrange to get $|x-7| = 3$

Step3: Solve absolute value equation

Split into two cases:
Case 1: $x-7 = 3$ → $x = 3 + 7 = 10$
Case 2: $x-7 = -3$ → $x = -3 + 7 = 4$

Step4: Find y-intercept (set x=0)

Set $x=0$, so $y = |0-7| - 3 = 7 - 3 = 4$

Answer:

x-intercept(s): $(4, 0)$ and $(10, 0)$
y-intercept: $(0, 4)$