Question

How do you write an equation in point slope form given (–1, 3) and (1, 7)?

Answer 1

I don't know what " point slope form" is but here's the equation
`y=2x+5`

Explanation:

If we have two points (-1,3) and (1,7) we can find the gradient (slope). We do this by finding the difference between the two
`y` values and divide this by the difference between the two `x` values

7-3=4 this is the difference in the `y` values

1--1=1+1=2 `=>` difference in `x` values

Gradient `=4/2` =2

The equation of the line is `y=2x+c` where the c value is the `y` intercept.( the place it crosses the `y` axis)

Substitute (1,7) into the equation to find c

7=`2xx1`+c

7=2+c

5=c

Put this into the equation in place of c

Answer 2

`y-7=2(x-1)`

Explanation:

`"the equation of a line in "color(blue)"point-slope form"` is.

`•color(white)(x)y-y_1=m(x-x_1)`

`"where m is the slope and "(x_1,y_1)" a point on the line"`

`"to calculate m use the "color(blue)"gradient formula"`

`•color(white)(x)m=(y_2-y_1)/(x_2-x_1)`

`"let "(x_1,y_1)=(-1,3)" and "(x_2,y_2)=(1,7)`

`rArrm=(7-3)/(1-(-1))=4/2=2`

`"use either of the 2 given points as a point on the line"`

`"using "(x_1,y_1)=(1,7)" then"`

`rArry-7=2(x-1)larrcolor(red)"in point-slope form"`