Question

Write equations (both, Point Slope & Slope Intercept Forms) of the line with

slope of -2 and point (9,2).

Answer 1

Equation of line in Point Slope Form is
`\mathbf{y-2=-2(x-9)}`

Equation of line in Slope Intercept Form is:
`\mathbf{y=-2x+20}`

Explanation:

We need to write equation of line having slope -2 and point (9,2)

a) Equation in Point Slope Form

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

Where x₁ and y₁ are the points of line and m is slope.

x₁=9 and y₁=2 and m=-2

Putting values in formula and finding equation:

`y-y_1=m(x-x_1)\\y-2=-2(x-9)`

So, Equation of line in Point Slope Form is
`\mathbf{y-2=-2(x-9)}`

b) Equation in Slope Intercept Form

The general equation of Slope Intercept Form is:
`y=mx+b`

where m is slope and b is y-intercept

Finding y-intercept using slope m=-2 and point(9,2)

`y=mx+b\\2=-2(9)+b\\2=-18+b\\b=2+18\\b=20`

The equation in slope m=-2 and b=20 is:

`y=mx+b\\y=-2x+20`

So, equation of line in Slope Intercept Form is:
`\mathbf{y=-2x+20}`