Answer:
[tex]y = \frac{17}{15}x + \frac{16}{15}[/tex]
Step-by-step explanation:
So the slope-intercept form is given as: y=mx+b where m is the slope and b is the y-intercept (since if you plug in 0 as x, mx will be 0 leaving only b). You can calculate the slope with the slope formula: [tex]slope=\frac{y_2-y_1}{x_2-x_1}[/tex] which is essentially [tex]\frac{rise}{run}[/tex]. So for this example (-8, -8) will be ([tex]x_1, y_1[/tex]) and (7, 9) will be ([tex]x_2, y_2[/tex]).
Plug values into equation:
[tex]\frac{9 - (-8)}{7 - (-8)}[/tex]
cancel out negatives
[tex]\frac{9+8}{7+8}\\[/tex]
Simplify
[tex]\frac{17}{15}[/tex]
The fraction is in the most simplified form unless you want to have a mixed fraction, otherwise you can't do anything else to the fraction.
so now we have the slope we have one part of the equation: [tex]y=\frac{17}{15}x + b[/tex], but now we need to solve for b. This can be done by using either of the points and plugging in x and y, but for this example I'll use (7, 9).
Plug in (7, 9) as (x, y)
[tex]9 = \frac{17}{15}(7) + b[/tex]
Multiply
[tex]9 = \frac{119}{15}+b[/tex]
Subtract
[tex]9-\frac{119}{15}=b[/tex]
Rewrite 9 as a fraction
[tex]\frac{135}{15} - \frac{119}{15} = b[/tex]
Subtract numerators
[tex]\frac{16}{15} = b[/tex]
now we have both pieces of information
[tex]y = \frac{17}{15}x + \frac{16}{15}[/tex]
