Question

The table represents a linear equation.which equation shows how (-10,8) can be used to write the equation of this line is point-slope form?

Answer 1

`\large\boxed{y-8=-0.2(x+10)}`

Explanation:

The point-slope form of an equation of a line:

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

m - slope

(x₁, y₁) - point

The formula of a slope:

`m=(y_2-y_1)/(x_2-x_1)`

From the table we have the points (-10, 8) and (10, 4). Substitute:

`m=(4-8)/(10-(-10))=(-4)/(20)=-(1)/(5)=-0.2`

The equation of a line:

`y-8=-0.2(x-(-10))\\\\y-8=-0.2(x+10)`

Answer 2

The answer is
`y-8=-0.2*(x+10)\\\\`

Explanation:

In order to determine the correct option, we have to know about point-slope form.

The point-slope form is the way that we can create linear functions from a point and a slope. The formula is:

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

Where:

`(x_1,y_1)\\\\`: Coordinates of the point.

m: Slope

Also we can get the slope from two points. The formula is:

`m=(y_2-y_1)/(x_2-x_1)`

`(x_1,y_1)\\\\`: Coordinates of the first point.

`(x_2,y_2)\\\\`: Coordinates of the second point.

So first we determine the slope:

`P_1=(x_1,y_1)=(-10,8)\\P_2=(x_2,y_2)=(-5,7)\\\\m=(7-8)/(-5-(-10))\\m=(-1)/(5)=-0.2\\\\\\`

Finally, the correct option is:

`y-8=-0.2*(x+10)\\\\`