Question

1) What is the equation, in point-slope form, for a line that goes through (8,−4) and has a slope of −5/6 ?

Answer 1

Answer:

The answers are:

1)  y + 4 = -5/6(x - 8), which is A, the first option.

2)  y - 1 = 5/6(x + 8), which is D, the last option.

3)  y + 1 = 6/11(x + 4), which is option C, the third option

4) - y + 3 = -12/7(x - 5), which is option B, the second from the top

5) Plot these points on a graph:

(-1, 5 1/2)

(0, 5 1/4)

(1, 5)

(2, 4 3/4)

Step-by-step explanation:

Question 1:

y - y1 = m(x - x1)

y - (-4) = -5/6(x - 8)

y + 4 = -5/6(x - 8), which is A, the first option.

Question 2:

y - y1 = m(x - x1)

y - 1 = 5/6(x - (-8))

y - 1 = 5/6(x + 8), which is D, the last option.

Question 3:

m = (y - y1)/(x - x1)

m = (5 - (-1)) / (7 - (- 4))

m = (5 + 1) / (7 + 4)

m = 6 / 11

Use the point slope equation and (-4, -1), substitute:

y - y1 = m(x - x1)

y - (-1) = 6/11(x - (-4))

y + 1 = 6/11(x + 4), which is option C, the third option

Question 4:

m = (y - y1)/(x - x1)

m = (-3 - 9)/(5 - (- 2))

m = -12 / (5 + 2)

m = -12/7

Use the point slope equation and (5, -3), substitute:

y - y1 = m(x - x1)

y - (-3) = -12/7(x - 5)

y + 3 = -12/7(x - 5), which is option B, the second from the top

Question 5:

Solve for y, then calculate a few points, graph those points:

y - 4 = -1/4(x - 5)

y - 4 = -1/4x + 5/4

y = -1/4x + 5/4 + 4

y = -1/4x + 5/4 + 16/4

y = -1/4x + 21/4

Solve for x =  -1, 0, 1, 2:

f(-1) = -1/4(-1) + 21/4 = 1/4 + 21/4 = 22/4 = 5 1/2, giving point (-1, 5 1/2)

f(0) = 21/4 or 5 1/4 giving point (0, 5 1/4)

f(1) = -1/4 + 21/4 = 20/4 = 5, giving point (1, 5)

f(2) = -1/4(2) + 21/4 = -2/4 + 21/4 = 19/4 or 4 3/4, giving point (2, 4 3/4)