Question

this question has two parts. use the graph to answer part a and part b.
part a
what is the slope of the line? enter the answer in the box.
the slope is
part b
what is the value of x? enter the answer in the box.
x =

Explanation:

Step1: Calculate slope from rise/run

Slope $m = \frac{\text{rise}}{\text{run}} = \frac{10}{8} = \frac{5}{4}$

Step2: Define line equation using y-intercept

The y-intercept is $(0,6)$, so the line equation is $y = \frac{5}{4}x + 6$

Step3: Solve for $x$ when $y=21$

Substitute $y=21$ into the equation:
$21 = \frac{5}{4}x + 6$
Subtract 6 from both sides:
$21 - 6 = \frac{5}{4}x$
$15 = \frac{5}{4}x$
Multiply both sides by $\frac{4}{5}$:
$x = 15 \times \frac{4}{5} = 12$

Answer:

Part A: $\frac{5}{4}$
Part B: $12$