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

Apr 11, 2018

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

#### 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 $\implies$ difference in $x$ values

Gradient $= \frac{4}{2}$ =2

The equation of the line is $y = 2 x + c$ 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=$2 \times 1$+c

7=2+c

5=c

Put this into the equation in place of c

Apr 11, 2018

$y - 7 = 2 \left(x - 1\right)$

#### Explanation:

$\text{the equation of a line in "color(blue)"point-slope form}$ is.

•color(white)(x)y-y_1=m(x-x_1)

$\text{where m is the slope and "(x_1,y_1)" a point on the line}$

$\text{to calculate m use the "color(blue)"gradient formula}$

•color(white)(x)m=(y_2-y_1)/(x_2-x_1)

$\text{let "(x_1,y_1)=(-1,3)" and } \left({x}_{2} , {y}_{2}\right) = \left(1 , 7\right)$

$\Rightarrow m = \frac{7 - 3}{1 - \left(- 1\right)} = \frac{4}{2} = 2$

$\text{use either of the 2 given points as a point on the line}$

$\text{using "(x_1,y_1)=(1,7)" then}$

$\Rightarrow y - 7 = 2 \left(x - 1\right) \leftarrow \textcolor{red}{\text{in point-slope form}}$