Question

How do you write an equation of a line that passes through (4,9) , (-2,-6)?

Answer 1

I will use the point-slope form of a line (`y-y_1=m(x-x_1)`):

Point 1 will be (4,9)
Point 2 will be (-2,-6)

Calculating the slope: `m=(∆y)/(∆x)=(y_2-y_1)/(x_2-x_1)=(9-(-6))/(4-(-2))=(9+6)/(4+2)=15/6=(3(5))/(3(2))=color(red)(5/2)`

So: `y-(9)=(5/2)(x-4)`

Now, I will transform the equation from point-slope to slope-intercept (`y=mx+b`) form. Remember, changing the form of a line's equation does not change the line. It simply rewrites the variables in a different way.

`y-(9)=(5/2)(x-4)`
`y=(5/2)(x-4)+9`
`y=5/2x-20/2+9`
`y=5/2x-10+9`
`y=5/2x-1`