Question

If the slope of a line and a point on the line are known, the equation of the line can be found using the slope-intercept form, y=mx+b. To do so, substitute the value of the slope and the values of x and y using coordinates of the given point, the determine the value of b.

Using the above technique, find the equation of the line containing the points (-2,8) and (4,-1)
The equation of the line is ?

Answer 1

`y=((-3)/(2) )x + 5`

Explanation:

Only one thing you have to remember here and it is the equation for a linear line. This equation is:

`y-y_(0) = m(x-x_(0))`

Where m is the slope:

`m=(dy)/(dx) =(y_(2)-y_(1) )/(x_(2) -x_(1) )`

Writing the whole thing out using the given data points we get:

`y-8=((-1)-8)/(4-(-2)) (x-(-2))`

We then just have to equate this to an equation of the form y = mx + b:

⇒
`y=(-9)/(6) (x+2) + 8`

⇒
`y=((-3)/(2) )x+ ((-3)/(2))2 + 8`

⇒
`y=((-3)/(2) )x + (-3) + 8`

⇒
`y=((-3)/(2) )x + 5`

And there we go, our equation has been found.