Question

Given two ordered pairs (1,-2) and (3,-8), what is the equation of the line in slope-intercept form?

Answer 1

`y=-3x+1`

Explanation:

The general equation for a line in slope-intercept form is:

`y=mx+b`

where:
y = y-coordinate
m = slope
x = x-coordinate
b = y-intercept

To find the equation, first find the slope. The formula for slope is:

`m=(y_"2"-y_"1")/(x_"2"-x_"1")`

where:
m = slope
`(x_"1", y_"1")=(1,-2)`
`(x_"2", y_"2")=(3,-8)`

`m=(y_"2"-y_"1")/(x_"2"-x_"1")`

`m=((-8)-(-2))/((3)-(1))`

`m=-6/2`

`m=-3`

Rewrite the equation:

`y=-3x+b`

Now substitute a known point into the equation to solve for `b`:

`y=-3x+b`

`(-2)=-3(1)+b`

`-2=-3+b`

`1=b`

Final answer:

`y=-3x+1`