# How do you write an equation in point slope form that passes through (1,4) and(4,9)?

##### 2 Answers

#### Explanation:

We want this in the form

Gradient is the change in y over the change in x, or the rise over run; however you like to think about it.

So for our points

Now, by rearranging our equation for gradient, we can show that:

Here,

Since we know

as required.

An alternative method, after finding the gradient, is to substitute your gradient and a pair of points into

#### 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)=(1,4)" and "(x_2,y_2)=(4,9)#

#m=(9-4)/(4-1)=5/3#

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

#"using "(1,4)" then"#

#y-4=5/3(x-1)larrcolor(red)"in point-slope form"#