Suppose a line passes through the point (6 caps, $3/cap) and has a slope of -3. Which of the following points also lie along that line? Select all that apply.
a) 4 caps, $9/cap
b) 7 caps, $0/cap
c) 5 caps, $5/cap
d) 2 caps, $7/cap
e) 7 caps, $1/cap
f) 4 caps, $5/cap
My answer: a, c, e
Am I correct?
If the line is
3=-3*6+b
b=21 so
$/cap=-3(caps)+21
a) 9=-3(4)+21=-12+21=9 checks
b) 0=-3(7)+21=0 checks
c) 5=-3(5)+21=6 does not check
You can check the rest.
(0-8/5)is a solution of 2x-5y=7 is/not how
To determine which points lie along a line with a given slope and passing through a given point, we can use the equation of a line in point-slope form.
The equation of a line passing through the point (x₁, y₁) with a slope of m is:
y - y₁ = m(x - x₁)
Given that the line passes through the point (6 caps, $3/cap) and has a slope of -3, we can write the equation of the line as:
y - 3 = -3(x - 6)
Now we can check which of the given points satisfy this equation to identify the points that lie on the line.
a) Plug in the values (4 caps, $9/cap):
9 - 3 = -3(4 - 6)
6 = 6
The equation is satisfied.
b) Plug in the values (7 caps, $0/cap):
0 - 3 = -3(7 - 6)
-3 = -3
The equation is satisfied.
c) Plug in the values (5 caps, $5/cap):
5 - 3 = -3(5 - 6)
2 = 3
The equation is not satisfied.
d) Plug in the values (2 caps, $7/cap):
7 - 3 = -3(2 - 6)
4 = 12
The equation is not satisfied.
e) Plug in the values (7 caps, $1/cap):
1 - 3 = -3(7 - 6)
-2 = -3
The equation is satisfied.
f) Plug in the values (4 caps, $5/cap):
5 - 3 = -3(4 - 6)
2 = 6
The equation is not satisfied.
Based on these calculations, the points that lie on the line are:
a) 4 caps, $9/cap
b) 7 caps, $0/cap
e) 7 caps, $1/cap
Therefore, your answer of a, b, and e is correct.