Question

Which point is a solution for y = 3x - 5?

A. (-1, 3)
B. (4, 7)
C. (2, -1)
D. (3, -5)

Answer 1

Answer: B. (4,7)

Explanation

Let's try the coordinates of choice A.

Plug in x = -1 and y = 3.

y = 3x-5

3 = 3*(-1) - 5

3 = -3 - 5

3 = -8

The last equation is false, so the first equation is false when x = -1 and y = 3.

If choice A said (-1,-8) then it would be a point on this line. We can rule out choice A.

Now try choice B

y = 3x-5

7 = 3*4 - 5

7 = 12 - 5

7 = 7

We arrive at a true statement, so y = 3x-5 is true when x = 4 and y = 7. This confirms the point (4,7) is on the line y = 3x-5, and confirms it is a solution.

Use a graphing tool like Desmos to confirm. GeoGebra is another good option.

Choices C and D are similar to choice A. They can be ruled out.

Answer 2

Answer: B. (4, 7)

Explanation:

We will substitute every x-coordinate into the function and see if the correct corresponding y-value is the result. If it isn't, it's not a solution. If it is, it's a solution.

A - ✗

y = 3x - 5

? = 3(-1) - 5

? = -3 -5

3 ≠ -8

B - ✔

y = 3x - 5

? = 3(4) - 5

? = 12 - 5

7 = 7

C - ✗

y = 3x - 5

? = 3(2) - 5

? = 6 - 5

-1 ≠ 1

D - ✗

y = 3x - 5

? = 3(3) - 5

? = 9 - 5

-5 ≠ 4

This gives us the coordinate point that is a solution for y = 3x - 5, the answer is B. (4, 7).