Answer:
a) y = 4/3x + 26/3
b) 4x - 3y + 26 = 0
c) x-int: (-6 1/2, 0)
y-int: (0, 8 2/3)
Step-by-step explanation:
a) to get points into the point-slope form you first find the slope by taking the difference of the y-values over the difference of the x-values;
slope (m) = (6 - 2) / (-2 - -5) = 4/3
plug 4/3 into 'm' and select one of the two points to plug in their 'x' and 'y' values so you can find 'b' (the y-intercept)
y = mx + b
6 = 4/3(-2) + b
6 = -8/3 + b
b = 6 + 8/3 = 18/3 + 8/3 or 26/3 (or 8.67)
so, put it all together to get the p-s form of y = 4/3x + 26/3
b) general equation is Ax + By + C = 0
take y = 4/3x + 26/3 and multiply each side by 3 to remove denominators
you get: 3y = 4x + 26; rearrange to get 4x - 3y + 26 = 0
c) y-intercept is (0, 8 2/3); derived during step (a)
to get x-intercept, plug zero in for 'y' and solve for 'x':
0 = 4/3x + 26/3
-4/3x = 26/3
cross-multiply and get 12x = -78
x = -78/12 or -39/6 or -6 1/2
