Question

write an equation of the line in the point- slope form that passes through the given points in the table. Then write the equation in slope-intercept form. (10,80) (15,95)

Answer 1

We know that the line passes through the points (10,130) and (20,200).

First, we have to find the slope with the following formula

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

Where,

`\begin{gathered} x_1=10 \\ ^{}x_2=15^{} \\ y_1=80 \\ y_2=95 \end{gathered}`

Replacing these coordinates, we have

`m=(95-80)/(15-10)=(15)/(5)=3`

The slope is 7.

Now, we use one point, the slope, and the point-slope formula to find the equation

`\begin{gathered} y-y_1=m(x-x_1) \\ y-80=3(x-10) \end{gathered}`

Therefore, the point-slope form of the line is

`y-80=3(x-10)`