Question

What is an equation of the line that passes through the points (1, 2)(1,2) and (2, -1)(2,−1)?

Answer 1

y = -3x + 4

Explanation:

First, we find the slope, and to find the slope;
`(y_(2) - y_(1))/(x_(2) - x_(1) )`

Slope : -3

Now we fill in the equation with a point and find the y- intercept:

2 = -3(1) + b

2 = -2 + b

4 = b

y = -3x + 4

Answer 2

`y = - 3x + 5`

Explanation:

to find the gradient/slope between these points:

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

`( - 1 -2)/(2 - 1) = - 3`

the gradient is -3

we need to write the equation in the form y=mx+c. Choose any of the two coordinates in the question. I'll choose (1,2).

y is 2, x is 1 and m is the gradient which is -3

working out c:

`y = mx + c`

`2 = - 3(1) + c`

`2 = - 3 + c`

add 3 on both sides

`2 + 3 = c`

`c = 5`

final equation:

`y - = - 3x + 5`