Question

Passes through (-2, 1) and (2, -5)
I need to find the y=mx+b

Answer 1

`y = (-3/2)\, x + (-2)`.

Explanation:

If
`(x_(0),\, y_(0))` is on the equation of the line
`y = m\, x + b`, then substituting
`x = x_(0)` and
`y = y_(0)` into the equation would still give an equality:
`y_(0) = m\, x_(0) + b`.

In this question, since
`(-2,\, 1)` is a point on the line
`y = m\, x + b`, equality shall still hold after substituting in
`x = (-2)` and
`y = 1`:

`1 = m* (-2) + b`.

Similarly, since
`(2,\, -5)` is a point on this line, equality shall still hold after substituting in
`x = 2` and
`y = (-5)`:

`(-5) = m* 2 + b`.

The unknowns of both equations are
`m` and
`b`.

Solve this system of two equations and two unknowns:

`\left\lbrace\begin{aligned}& (-2)\, m + b = 1\\ & 2\, m + b = (-5)\end{aligned}\right.`.

`\left\lbrace\begin{aligned}& m = -(3)/(2) \\ & b = -2\end{aligned}\right.`.

Therefore, the equation of this line would be:

`y = (-3/2)\, x + (-2)`.