Write the equation of the line that passes through the points (-2, 3) and (-2, 5).

Question

A. y=5

B. y= −2

C. y=1/2​x+1

D. x= −2

Answer 1

Let’s take a look. When we are trying to find an equation from two points there are two steps, first find the slope and then sole for the equation.

To find the slope we use the equation of (y₂-y₁)/(x₂-x₁). So plug into the equation the two points. (3-5)/(-2- (-2)).

Simplify to (-2)/0. Do you notice something about this slope? What does it mean when we have zero on the bottom?

When you think about what the fraction means, it stands for rise/run so this slope goes down two but over 0.

This means it is a vertical line, its slope is undefined. When a slope is undefined it has an unlimited number of y values and only 1 x value. based on the points what is the x value.

Which answer gives just an x value? What value is that?

Answer 2

Note that the x-coordinate is the same for both points, so you have a line of constant x, i.e. a vertical line. Its equation is

x = -2

Answer 3

You have equations. Plug in the x and y values and see which works for both points.

y = 5

(-2,3) -----> 3 = 5.

(-2,5) ------> 5 = 5

Well, it's not A, because 3 ≠ 5.