Question

Write the equation of the line that passes through the points (7,-8) and (2, -8).

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

Answer 1

The equation of the line that passes through the points (7,-8) and (2, -8) is
`\mathbf{y=-8}`

Explanation:

We need to write the equation of the line that passes through the points (7,-8) and (2, -8).

We need to write answer in fully reduced point-slope form, unless it is a vertical or horizontal line.

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

where m is slope of the line.

To find the slope, we can use formula:
`Slope=(y_2-y_1)/(x_2-x_1)`

We have
`x_1=7,y_1=-8,x_2=2, y_2=-8`

Putting values and finding slope:

`Slope=(y_2-y_1)/(x_2-x_1)\\Slope=(-8-(-8))/(2-7)\\Slope=(-8+8)/(-5)\\Slope=(0)/(-5)\\Slope=0`

So, we find the slope : m = 0

Now, using the point (7,-8) and slope m =0, the required equation is:

`y-y_1=m(x-x_1)\\y-(-8)=0(x-7)\\y+8=0\\y=-8`

So, the equation of the line that passes through the points (7,-8) and (2, -8) is
`\mathbf{y=-8}`