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).