Quick question! (multiple choice) HELP please?

Question

Find the point on the line y = -3x + 5 that is closest to the point (2, -2).

a) (-3, 14)
b) (2.3, -1.9)
c) (1.1, 1.7)
d) (2.3, 0.32)

Answer 1

You want the line that is perpendicular to your line that passes through (2,-2): y=(1/3)x-(8/3).
Now find out where the two lines intersect by solving the following equation: -3x+5=(x-8)/3 or -9x+15=x-8
or -10x=-23 or x=2.3; now solve for y: y=-3*(2.3)+5=-1.9.
So your answer is (2.3,-1.9).

Answer 2

One way to do this, is first find line that has perpendicular
slope of equation. Since slope is -3, the slope perpencilaur to this is -1/-3 = 1/3.
So, equation is y=(1/3)x+b.
Now find the line that has the points (2,-2).
SO, plug in (2,-2), giving you -2=( 1/3)*(2)+b, so b=-2-2/3=-8/3.
SO, the line is y=(1/3)x-8/3.
So, now you just have to find intersection of this line
and y=-3x+5.
So, -3x+5=(1/3)x-8/3, or (-10/3)x=-23/3, so, x=2.3.
So, then just plug this in y=-3x+5, giving you y=-3*2.3+5=-1.9.

So, the answer is b)(2.3,-1.9)

Answer 3

To find the closest point, draw a line through the point that is perpendicular to the line. Using the point-slope formula:
y-y1=m(x-x1)
Since the two lines are perpendicular, the product of their slopes must be -1. So m=-1/3. Y1 and x1 come from the given point.
y-(-2)=(1/3)(x-2)
y+2=(1/3)x-2/3
y=(1/3)x-8/3
Find the intersection of this line with the first line.
(1/3)x-8/3=y=-3x+5
x-8=-9x+15
10x=23
x=2.3
y=-3*2.3+5=-1.9

So, the answer is (2.3,-1.9), choice (b).

Answer 4

B because as u can see 2.3 and -1.9 are the closest to 2 and -2

Answer 5

D. simply by fact Jupiter is made ordinarily of gas and it rotates at as quickly as. D. in the middle of the planet B. ecosystem containing ordinarily hydrogen and helium No, i'm unlikely to make a remark. No, i'm no longer.

Answer 6

Plug and chug all and see what you get in return.

Answer 7

b

Answer 8

Answer (b)