Hey there!!
Slope-intercept form : y = mx + b
Equation given : y = kx + b
Hence, we know k = slope and b is the y-intercept
How, do we find slope?
Formula : [tex]\frac{y2-y1}{x2-x1}[/tex]
We have got two co-ordinates : ( 2 , 10 ) and ( -7 , -10 )
Plugging in the values : [tex]\frac{-10-10}{-7-2}[/tex]
Simplifying it : [tex]\frac{20}{9}[/tex]
Hence, the slope we got is : [tex]\frac{20}{9}[/tex]
Now, lets plug in this value in the equation y = kx + b
k is 20/9
Plugging in :
... [tex]y = \frac{20x}{9} + b[/tex]
Now let's take a co-ordinate and plug it in...
... [tex]10 = \frac{2*20}{9} + b[/tex]
... [tex]90 = 40 + b[/tex]
... [tex]b = 50[/tex]
... y-intercept is 50.
Now, let's get the whole equation in place...
... [tex]y = \frac{20x}{9} + 50[/tex]
Hope my answer helps!!
