Question

What is the equation for the line

Answer 1

The model equation for any line is
y = mx + b,
where m is slope and b is y-intercept (where the line intersects the y-axis).

The slope is change in y over change in x. You can find the slope by picking two points. The numerator will be the difference in y-coordinates, and the denominator will be the difference in x-coordinates.
As an equation, this is
slope =
`(y2-y1)/(x2-x1)`,
where the two points are (x1, y1) and (x2, y2).

Let's pick two points to find the slope: (0, 5) and (3, -7).
The slope is

`(-7-5)/(3-0) = (-12)/(3) = -4`

Now that we have the slope m = -4, we need to find the y-intercept b. The line crosses the y-axis at 5, so b = 5.

The equation is y = -4x + 5