Slope-intercept form is \(\sf~y=mx+b\), where \(\sf~m\) is the slope and \(\sf~b\) is the y-intercept.
Slope = -3, y-intercept = -1
Plug in what we know:
\(\sf~y=mx+b\)
\(\sf~y=-3x-1\)
Slope = -2, y-intercept = -4
Plug in what we know:
\(\sf~y=mx+b\)
\(\sf~y=-2x-4\)
Through: (-3,2) , slope=-1/3
Okay, here we use point-slope form, and the simplify to get it in slope-intercept form.
\(\sf~y-y_1=m(x-x_1)\)
Where \(\sf~y_1\) is the y-value of the point, \(\sf~x_1\) is the x-value of the point, and \(\sf~m\) is the slope.
Plug in what we know:
\(\sf~y-2=-\dfrac{1}{3}(x+3)\)
Distribute -1/3 into the parenthesis:
\(\sf~y-2=-\dfrac{1}{3}x-1\)
Add 2 to both sides:
\(\sf~y=-\dfrac{1}{3}x+1\)
Through: (3,2) and (0,-5)
Now we plug this into the slope-formula to find the slope, plug the slope and one of these points into point-slope form, then simplify to get it in slope-intercept form.
\(\sf~m=\dfrac{y_2-y_1}{x_2-x_1}\)
(3, 2), (0, -5)
x1 y1 x2 y2
Plug in what we know:
\(\sf~m=\dfrac{-5-2}{0-3}\)
Subtract:
\(\sf~m=\dfrac{-7}{-3}\)
\(\sf~m=\dfrac{7}{3}\)
Plug this into point-slope form along with any point.
\(\sf~y-y_1=m(x-x_1)\)
\(\sf~y-2=\dfrac{7}{3}(x-3)\)
Distribute 7/3 into the parenthesis:
\(\sf~y-2=\dfrac{7}{3}x-7\)
Add 2 to both sides:
\(\sf~y=\dfrac{7}{3}x-5\)
x-5y-5=0
Add 5 to both sides:
\(\sf~x-5y=5\)
Subtract 'x' to both sides:
\(-5y=-x+5\)
Divide -5 to both sides:
\(\sf~y=\dfrac{1}{5}x-1\)
