What is the quation?

Question

What is the equation of a line passing through (-2,1) and (7,-3)?

Answer 1

There are two things you need to write the formula of a line: the slope of the line and a point that the line passes through.

To find the slope, take the difference in the y-coordinates divided by the difference in the x-coordinates.

(x1,y1) = (-2,1)
(x2,y2) = (7,-3)

slope: m = (y2 - y1) / (x2 - x1)
m = (-3 - 1) / (7 - (-2))
m = -4 / 9
This is the slope of the line.

Next, use Point-Slope form of a line to find the equation...

y - y1 = m(x - x1)
You know m, plug in the point (x1,y1)...

y - 1 = (-4/9)*(x - (-2))
y - 1 = (-4/9)*(x + 2)
y = (-4/9)*(x + 2) + 1
y = (-4/9)x - (8/9) + 1
y = (-4/9)x + (1/9)

That's the equation.
:-)

Answer 2

First, find the gradient by calculating rise/run.

[1-(-3)/(-2-7) = -4/9

Therefore, the equation of the line is
y = (-4/9) x + C

To find C, substitute in the x and y value of a given coordinate. In this case, I'll use x = 7 and y = -3.

-3 = (-4/9)(7) + C
C = -1/9

Therefore, the equation is
y = (-4/9)x + 1/9

Answer 3

The slope is (-3-1)/(7- -2)=-4/9
Now just use point slope formula: y-1=(-4/9)(x+2)
or y=-4/9x+1/9