Question

select the correct answer.
this week, theo walked x hours at a constant rate of 4 miles per hour and jogged y hours at a constant rate of 6 miles per hour. the total distance he walked and jogged this week was 36 miles. the relationship is modeled by this equation:
4x + 6y = 36.
which statement is true about the graph of this relationship?
a. the graph is a line that goes through the points (9,0) and (0,6).
b. the graph is a line that goes through the points (6,0) and (0,9).
c. the graph is a line that goes through the points (-9,0) and (0,6).
d. the graph is a line that goes through the points (-6,0) and (0,9).

Explanation:

Step1: Find x-intercept (y=0)

Substitute \( y = 0 \) into \( 4x + 6y = 36 \):
\( 4x + 6(0) = 36 \)
\( 4x = 36 \)
\( x = 9 \)
So x-intercept is \( (9, 0) \).

Step2: Find y-intercept (x=0)

Substitute \( x = 0 \) into \( 4x + 6y = 36 \):
\( 4(0) + 6y = 36 \)
\( 6y = 36 \)
\( y = 6 \)
So y-intercept is \( (0, 6) \).

Answer:

A. The graph is a line that goes through the points (9,0) and (0,6).