Question

Find the slope-intercept form of the equation of each of the following lines.

Passes through (6, 4) and has slope =1/2

Answer 1

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

Explanation:

Hi there!

Slope-intercept form:
`y=mx+b` where m is the slope and b is the y-intercept

We're given that the slope is
`\displaystyle(1)/(2)`. Plug this into
`y=mx+b`:

`y=\displaystyle(1)/(2)x+b`

Now, to solve for the y-intercept, plug in the point (6,4) and solve for b:

`4=\displaystyle(1)/(2)(6)+b\\\\4=3+b\\b=1`

Therefore, the y-intercept of the line is 1. Plug this back into
`y=\displaystyle(1)/(2)x+b`:

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

I hope this helps!