Question

Find the point-slope equation . use first point in your equation

Answer 1

Given:

`The\text{ given points are \lparen-10,-20\rparen and \lparen1,-9\rparen.}`

Required:

We need to find the point-slope equation of the line that passes through the given points.

Step-by-step explanation:

Consider the point-slope form of the equation.

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

Consider the slope formula.

`m=(y_2-y_1)/(x_2-x_1)`
`Substitute\text{ }y_2=-9,y_1=-20,x_2=1,\text{ and }x_1=-10\text{ in the slope formula.}`
`m=(-9-(-20))/(1-(-10))`
`m=(-9+20)/(1+10)`
`m=(11)/(11)`
`m=1`

Use the first point (-10,-20) in the point-slope equation.

`Substitute\text{ }m=1,\text{ }x_1=-10,\text{ and }y_1=-20\text{ in the point-slope form of equation}`

`y-(-20)=(1)(x-(-10))`

Final answer:

`y-(-20)=(1)(x-(-10))`