50 points! a. Use the Point-Slope form to find the equation of the line through the points (-5, 2) and (-2, 6).

b. Write the equation from part (a) above into the General as well as the slope-intercept form showing every step.

c. Find the x and y-intercepts of the equation above.

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

10 glasses of juice could be made with 5 carrots, 1,500 orange juice, 2,000 papaya juice.

b

step-by-step explanation: