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.
