What is the equation of a line passing through the points $(0,4)$ and $(2,5)$?

Summary Submit Skip Question

First, find the slope between the two points using the slope formula.

$$m=\frac{y_2-y_1}{x_2-x_1}$$

Using $(0,4)$ as $(x_1,y_1)$ and $(2,5)$ as $(x_2,y_2)$, we have

$$m=\frac{5-4}{2-0}=\frac{1}{2}$$

Plug these into the point-slope formula using either of the points.

$$y-y_1=m(x-x_1)$$

If we use the point $(0,4)$ and the slope $(m=\frac{1}{2})$, we obtain:

$$y-4=\frac{1}{2}(x-0)$$ $$y-4=\frac{1}{2}x$$ $$y=\frac{1}{2}x+4$$

Similar to the first approach, we first find the slope of the equation by using the two points.

$$m=\frac{1}{2}$$

We plug the slope and a point into the slope-intercept formula.

$$y=mx+b$$

Using the point $(0,4)$ and $m=\frac{1}{2}$, we obtain

$$4=\frac{1}{2}(0)+b$$ $$4=b$$

We use the slope and y-intercept to write the equation.

$$y=\frac{1}{2}x+4$$

To check if several points are on the same line, simply plug the points into the answer choices. If we go from top to bottom, we get lucky, the first answer choice works.