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