Question

Determine the equation of the line that passes through the given points. (If you have a graphing calculator, you can use the table feature to confirm that the coordinates of both points satisfy your equation.)

(10, 2) and (-3, 2)
a.
y = 2 x
b.
y = 2 x minus 3
c.
y = 2
d.
y = 2 x + 10



Please select the best answer from the choices provided


A
B
C
D

Answer 1

c). y = 2

Explanation:

We can check a line by inputting the x and y from (x, y) into the equation.

For a. y = 2x we get

2 = 2*10 and 2 = 2*(-3), both of those are false

For b. y = 2x - 3 we get

2 = 2*10 - 3 and 2 = 2*(-3) + 10, both of those are false again

For c. y = 2 we get

2 = 2 and 2 = 2, both of those are true, so this is the right answer.

For d. y = 2x + 10 we get

2 = 2*10 + 10 and 2 = 2*(-3) + 10, both of those are false

Alternatively, we can solve the equation y = ax + b (this gives a single answer for any two points with different x's).

y = ax + b

We input (x, y) as (10, 2) and (-3, 2)

2 = a*10 + b = 10a + b

2 = a*(-3) + b = b - 3a

so we have

10a + b = b - 3a

13a = b - b

13a = 0

a = 0

Now we ca use a = 0 to solve either of the equations above:

2 = 10a + b

2 = 10*0 + b

2 = b

so with a=0 and b=2 we get the answer

y = 0*x + 2

y = 2

Which brings us to answer c. again.