Question

What is the equation in point slope form of the line that passes through the points (7, 5) and (-4, 1)?

Answer 1

`y-5=4/11(x-7)`

Explanation:

We start by first finding the slope by using the slope formula:

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

If we let `(7,5)->(color(red)(x_1),color(blue)(y_1))` and `(-4,1)-> (color(red)(x_2),color(blue)(y_2))` then:

`m=color(blue)(1-5)/color(red)(-4-7)=-(4)/-11=4/11`

Now that we have the slope, we can find the equation of the line in point-slope formula:

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

where `m` is the slope and `x_1` and `y_1` is a coordinate on the line. I will use the point: `(7,5)`

The equation in point-slope form is then:

`y-5=4/11(x-7)`