Question

If a line contains the point (0, 1) and has a slope of 2, then which of the following points also lies on the line? (1,3) (3,1) (2,2) (2,3)

Answer 1

(1,3)

Explanation:

Linear equations are typically organized in slope-intercept form:
`y=mx+b` where m is the slope and b is the y-intercept (the value of y when the line crosses the y-axis, or when x is equal to 0).

We're given that this line contains the point (0,1). This tells us that the y-intercept (b) of the line is 1. We're also given that this line has a slope (m) of 2. Plug these values into
`y=mx+b`:

`y=2x+1`

Now, plug in all of the possible points to see which are solutions.

1) (1,3)

`3=2(1)+1\\3=2+1\\3=3`

Because the left side of the equation is equal to the right, (1,3) also lies on this line.

2) (3,1)

`1=2(3)+1\\1=6+1\\1=7`

Because the left side is not equal to the right, (3,1) does not lie on the line.

3) (2,2)

`2=2(2)+1\\2=4+1\\2=5`

Because the left side is not equal to the right, (2,2) does not lie on the line.

4) (2,3)

`3=2(2)+1\\3=4+1\\3=5`

Because the left side is not equal to the right, (2,3) does not lie on the line.

I hope this helps!