Question

The graph plots four equations, A, B, C, and D:

Answer 1

It is answer D

Line B and D.

Answer 2

None of these have this solution.

The only line that goes through (4, 8) is Line B.

Graphically, Line D is close, but still does not go through the point.

Explanation:

o write the equation for each line, we start with the slope. The formula for slope is:

$m=\frac{y_2-y_1}{x_2-x_1}$

Using the points for A, we have:

$m=\frac{16--4}{-6-9}=\frac{16+4}{-15}=\frac{20}{-15}=-\frac{4}{3}$

Using point-slope form,

y-y₁ = m(x-x₁),

we have:

y-16=(-4/3)(x--6)

y-16 = (-4/3)(x+6)

y-16 = (-4/3)(x)+(-4/3)(6)

y-16 = (-4/3)x + (-24/3)

y-16 = (-4/3)x - 8

Adding 16 to each side,

y-16+16 = (-4/3)x-8+16

y = (-4/3)x+8

Substituting 4 for x,

y = (-4/3)(4)+8

y = (-16/3)+8

y = -5 1/3 + 8

y = 2 2/3

This does not go through (4, 8).

For B, the slope is:

m = (20-0)/(-2-8)

m = 20/-10

m = -2

In point-slope form,

y-20 = -2(x--2)

y-20 = -2(x+2)

y-20 = -2(x)+(-2)(2)

y-20 = -2x-4

Adding 20 to each side,

y-20+20 = -2x-4+20

y = -2x+16

Substituting 4 for x,

y = -2(4)+16

y = -8+16

y = 8

This does go through (4, 8).

For C, the slope is

m = (-6-20)/(-7-16)

m = (-26)/(-13)

m = 2

In point-slope form,

y--6 = 2(x--7)

y+6 = 2(x+7)

y+6 = 2(x) + 2(7)

y+6 = 2x+14

Subtracting 6 from each side,

y+6-6 = 2x+14-6

y = 2x+8

Substituting 4 for x,

y = 2(4)+8

y = 8+8

y = 16

This does not go through (4, 8).

For D, the slope is

m = (20--7)/(7-0)

m = (20+7)/7

m = 27/7

Since it goes through (0, -7), the y-intercept is -7; in slope-intercept form, this is;

y = 27/7x - 7.

Substituting 4 for x,

y = (27/7)(4)-7

y = (108/7) - 7

y = 15 3/7 - 7

y = 8 3/7

This does not go through (4, 8) either.