Question

Write the equation of the line that passes through the points (5,0) and (-6, -1).

Put your answer in fully reduced point-slope form, unless it is a vertical or horizontal
line.

Answer 1

The equation in point-slope form is:
`\mathbf{y=(1)/(11)x-(5)/(11) }`

Explanation:

We need to find equation of line in point slope form that passes through points (5,0) and (-6, -1).

The general equation of point slope form is:
`\mathbf{y-y_1=m(x-x_1)}`

where m is the slope of line.

We need to know Slope m

Finding Slope m

Finding Slope m using formula:
`Slope=(y_2-y_1)/(x_2-x_1)`

We have
`x_1=5, y_1=0, x_2=-6 \ and \ y_2=-1`

Putting values and finding slope

`Slope=(-1-0)/(-6-(5))\\Slope=(-1)/(-6-5)\\Slope=(-1)/(-11)\\Slope=(1)/(11)`

So , slope m is:
`\mathbf{m=(1)/(11)}`

Using point (5,0) and slope m =1/22 the equation of point-slope form is:

`y-y_1=m(x-x_1)\\y-0=(1)/(11) (x-5)\\y=(1)/(11)x-(5)/(11)`

So, the equation in point-slope form is:
`\mathbf{y=(1)/(11)x-(5)/(11) }`