Find the equation of the linear function represented by the table below: x y 1 2 2 0 3 -2 4 -4?

x y
1 2
2 0
3 -2
4 -4

Slope is rise over run. Run is horizontal distance, left to right. Run is always positive because we always go left to right. Rise is the vertical change in that same distance. A negative rise means it drops.

The equation of a line is y = mx where m is the slope. That line passes through the origin. If you want it to pass through some point (a, b) you subtract the coordinates like this: y - b = m(x - a). That is the point-slope form, and you can rewrite it in other forms if it is convenient. You may do this with any point on the line. They all reduce to the same equation.

You are given that x runs 3 units from x=1 to x=4 and rises -6 units from y-2 to y=-4 so the slope is -6/3 = -2. We can choose any point to write the equation. They all give the same result.

y - 2 = -2(x - 1) point-slope form

y - 2 = -2x + 2

y = -2x + 4 slope-intercept form, m=-2 and intercept=4

y + 2x - 4 = 0 standard form, all variables on the left, no fractions, and zero or a constant on the right.