write an equation with a line through (-1,-9) (2,6)

Answer 1

Slope of the Line

First find the slope, which is change in y (Δy) divided by change in x (Δx).

Δy / Δx = (6 – (–9))/(2 – (–1)) = (6+9)/(2+1) = 15/3 = 5

Point-Slope Form

y – y₀ = m(x – x₀) is an equation for a line with a slope of m that passes through the point (x₀,y₀).

(This form of the equation for a line is called point-slope form.)

Using m = 5 (derived above) and (x₀,y₀) = either (–1,9) or (2,6) we can find the equation for the line.

Using the point (2,6) we have m = 5, x₀ = 2, and y₀ = 6 to plug into y – y₀ = m(x – x₀), which gives us

y – 6 = 5(x – 2) = 5x – 10

Adding 6 to both sides gives us the equation for the line in slope-intercept (y = mx + b) form.

Answer

The equation for the line is y = 5x – 4

Answer 2

First, find the slope. Using the slope formula is probably the best way to do this: m=(y2-y1)/(x2-x1)

Then, use the point-slope equation: y=m(x-x1)+y1

In this example, the slope turns out to be 5 and the equation is y=5x-4