Question

Write an equation of given line through the two points (4,1) (3,-1)

Answer 1

`y=2x-7`

Explanation:

The equation for a straight line is

`y=mx+c`

where m is the gradient and c is the y-intercept.

To have the full equation, we need to find m and c values.

To find m, the formula is

`(y_(2)-y_(1) )/(x_(2)-x_(1) )`

By substituting the two points (4,1) and (3,-1) into the formula, we get:

`m =(-1-1)/(3-4) \\m=(-2)/(-1) \\m=2`

Now we have
`y=2x+c`

To solve for c, substitute any of the two points in to the equation. Let's say we insert (4,1) into the equation:

`y=2x+c\\1=2(4)+c\\c=1-8\\c=-7`

Therefore, the full equation is

`y=2x-7`

Pro tip:

You can always substitute (4,1) or (3,-1) to check if the equation is correct.