Ok, slope intercept form is y = mx + b
They give the slope and y intercept in the first one. all you have to do is plug them in, giving you y = 1/3x -5
The second one they give you a graph. Using the two points given, (-5,1) and (0,-1), use the equation y2- y1/ x2 - x1 to find the slope.
1- - 1 / -5-0
2/-5 = m = slope
the y-intercept is (0, y) or in this case (0,-1)
Therefore, y = 2/-5x - 1
For the next one, all you got to do is turn the standard form into slope intercept form.
4x - 2y = 14
-4x -4x
-2y = -4x +14
-2y/-2 = -4x/-2 + 14/-2
y = 2x - 7
When you are given a point and slope, you want to use the . . .you guessed it! Point - slope form
y-y₁=m(x-x₁)
slope = -3
Point (-1,3)
y - 3 = -3 (x - - 1)
y - 3 = -3x -3
y = -3x + 0
or
y = -3x
The last one, you are given two points. Find the slope using y2-y1/x2-x1
(-4,-7) (8, -13)
-13 - - 7 / 8 - - 4
-6/12
-1/2 = m = slope
Now plug the slope and one of the points into point - slope form
y-y₁=m(x-x₁)
y - -7 = -1/2 (x - - 4)
y +7 = -1/2x -2
y = -1/2x - 9