Answer:
slope is [tex]\frac{3}{5}[/tex] ; slope-intercept form is y = [tex]\frac{3}{5}[/tex] x + [tex]\frac{13}{20}[/tex] ; point-slope form is 4 - 10 = [tex]\frac{3}{5}[/tex] (-2 - 8)
Step-by-step explanation:
first, we find the slope by using our points (8,10) and (-2,4)
to do so, you use the expression [tex]\frac{y1 - y2}{x1 - x2\\}[/tex] where (8,10) is point 1 and (-2,4) is point 2
this results in [tex]\frac{10-4}{8--2}[/tex]
10-4 is 6 and 8--2 is 10
which results in the slope of [tex]\frac{3}{5}[/tex]
now that we have the slope, we can solve for the y-intercept using the slope-intercept formula [y = mx +b]
we choose a point [im using (8,10)] and but the values in for x and y in the equation, which gives us 10 = 3/5 (8) + b , and solve for b
to solve for b, we start by dividing both sides by 8, resulting in 5/4 = 3/5 +b
then, subtract 3/5 from 5/4, resulting in 13/20 = b
To check the work, we use slope-intercept formula again [yeyyy]
y = 3/5x + 13/20 ; 4 = 3/5 (-2) + 13/20
i used my calculator to check, it's correct
SO: the slope-intercept form of the equation is y = [tex]\frac{3}{5}[/tex] x + [tex]\frac{13}{20}[/tex]
now we get to do the point-slope formula [yeyyyyyyyyyyy!!!]
point-slope formula is y - y1 = m (x - x1)
the slope [m] is [tex]\frac{3}{5}[/tex]
and we use any given point [im using (8,10) again, but any point should technically be correct] for y1 and x1
inputting our values, we get y - 10 = 3/5 (x - 8)
now, you use any other point for x and y to check the work
4 - 10 = 3/5 (-2 - 8)
-2 - 8 is -10, and 3/5 times -10 is -6, which is equal to 4 - 10
