Question

Which equation represents a line that passes though (5, 1) and has a slope of 1/2?

Answer 1

`\large\boxed{y-1=(1)/(2)(x-5)\leftarrow\text{point-slope form}}\\\boxed{y=(1)/(2)x-(3)/(2)\leftarrow\text{slope-intercept form}}\\\boxed{x-2y=3\leftarrow\text{standard form}}`

Explanation:

The point-slope of an equation of a line:

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

We have

the point
`(5,\ 1)\to x_1=5,\ y_1=1`

and the slope
`m=(1)/(2)`

Substitute:

`y-1=(1)/(2)(x-5)` use distributive property

`y-1=(1)/(2)x-(5)/(2)` add 1 to both sides

`y=(1)/(2)x-(3)/(2)` multiply both sides by 2

`2y=x-3` subtract x from both sides

`-x+2y=-3` change the signs

`x-2y=3`