Question

Write an equation in slope-intercept form of the line that passes through (4, 8) and (0, -2).

Answer 1

slope intercept form:\[\Large y=mx+b\] where m is slope,
& b is y-intercept....{i.e. b is y-value ...when x=0(graph hits y-axis)}

Answer 2

so, you can get b by plugging in (x,y)=(0,-2)\[-2=\cancel{m \times0}+b\]\[\implies \Large b=-2\]

Answer 3

\[m=slope={rise \over run}=rate\ of\ change = { change\ in\ y \over change\ in\ x}\]

Answer 4

\[m={-2-8 \over 0-4} = {10 \over -4} =\Large \frac 52\]
\[\Large \therefore\ y= \frac 52 x -2\]