Question

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

Answer 1

`y=(1)/(2)x+2`

Explanation:

We can find the slope by using the formula

`\text{slope}=(y_1-y_2)/(x_1-x_2)`.

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

`\text{slope}=(5-3)/(6-2)=(2)/(4)=(1)/(2).`

Therefore, the slope is
`(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=(1)/(2)x+b.`

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

`3=(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=(1)/(2)` and
`b=2`, so the equation is

`y=(1)/(2)x+2.`