slope intercept

Question

suppose a line goes through the points (3,1) and (-2,-9). Write the equation of the line. Determine the intercepts.

Answer 1

The equation of a line is in the form y=mx+b , where m is slope and b is y-intercept.  The slope is the distance in y-coordinates between the points over the distance in x-coordinates between the points.

 

m = (y₂ - y₁) / (x₂ - x₁)

m = (-9 - 1) / (-2 - 3)

m = -10 / -5

m = 2

 

So far the equation of the line is

 

y = 2x + b

 

 

Next, we plug in the coordinate (3, 1) into the equation to find b.

 

1 = 2(3) + b

 

1 = 6 + b

 

-5 = b

 

The equation of the line is

 

y = 2x - 5

 

 

There are two types of intercepts:

 

x-intercept is the point on the x-axis that has the coordinate (x, 0).

y-intercept is the point on the y-axis that has the coordinate (0, y).

 

 

To find the x-intercept, plug in y=0 into the equation of the line.

To find the y-intercept, plug in x=0 into the equation of the line.

 

You are now all set.