Question

What is the equation of the line that passes through the points (2,3) and (6,5)

Answer 1

Answer:

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

Step-by-step explanation:

We can find the slope by using the formula

$\text{slope}=\frac{y_1-y_2}{x_1-x_2}$.

Plugging in the points (2,3) and (6,5), we have

$\text{slope}=\frac{5-3}{6-2}=\frac{2}{4}=\frac{1}{2}.$

Therefore, the slope is $\frac{1}{2}.$ We can then write the line in slope-intercept form, which is $y=mx+b$ where $m$ is the slope and $b$ is the y-intercept.

We already found the slope, so we know the equation is of the form

$y=\frac{1}{2}x+b.$

We can now plug in either one of the points to find $b.$ Plugging in (2,3), we get

$3=\frac{1}{2}(2)+b$.

To solve for $b$, we can subtract 1 from both sides of the equation:

$3=1+b$

$b=3-1=2$.

Now, we have all the variables we need to write the equation in slope-intercept form. We know $m=\frac{1}{2}$ and $b=2$, so the equation is

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