Problem and answer:
a) what is the y intercept?
(0,8) is the y intercept because it crosses the y axis.
What is the flat rate?
We can see that the flat rate is 8, which is the y intercept.
b) Find the slope and write an equation for the line.
[tex] \quad\quad\quad\boxed{ \tt{m = \frac{rise}{run} = \frac{ y \tiny{2} \: \small{ - } \: y \tiny{1}}{x \tiny{2} \: \small{ - } \: x \tiny{1}} }}[/tex]
We will use the first 2 points in the graph which is (1,12) and (2,16).
[tex]\quad\quad\quad\boxed{ \tt{m = \frac{16 - 12}{2 - 1} }}[/tex]
[tex]\quad\quad\quad\boxed{ \tt{m = \frac{4}{1} }}[/tex]
[tex] \quad\quad\quad\boxed{ \color{green}\tt{m = 4}}[/tex]
The equation is:
[tex] \quad \quad \quad \boxed{ \tt{y = mx + b}}[/tex]
c) Jack has $22 for how many hours can he rent an e-bike?
Let's use the equation as formula:
[tex] \quad \quad \quad \boxed{ \tt{y = mx + b}}[/tex]
Let's y = 22, mx = 4 and b = 8.
[tex] \quad \quad \quad \boxed{ \tt{22 =4x + 8}}[/tex]
Let's subtract 8 from each side.
[tex] \quad \quad \quad \boxed{ \tt{22 - 8 = 4x + 8 - 8}}[/tex]
[tex] \quad \quad \quad \boxed{ \tt{14 = 4x \: \:\cancel{ \color{red}+ 8 - 8}}}[/tex]
Let's devide it by 4 to cancel out the number 4.
[tex]\quad \quad \quad \boxed{ \tt{ \frac{14 = \cancel4x}{ \cancel{4} }}}[/tex]
[tex]\quad \quad \quad \boxed{ \color{green} \tt{3.5 = x}}[/tex]
Hence the answer for this is 3.5 hours or 3h50m. It is approximately 4 hours.
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