determine the x and y intercept

Question

determine the x and y intercept for the equation of a line 3x-2y=5. draw this line 

Answer 1

the x intercept is defined as the point where the line crosses the x axis.  By definition, y = 0 at the point.

 

so, set y = 0

and

3x =5

x =5/3

 

"x-intercept" = (5/3, 0)

 

Now, use the same procedure, but set x = 0 and solve for y

 

You can plot the line by simply using a straight line that intercepts the 2 points---or convert the equation to slope-intercept form  (y = ax + b)

Answer 2

We want to get the given equation of the line into y=mx+b form, where m is slope and b is y-intercept.

 

 

Subtract 3x on both sides of equation.

 

-2y = -3x + 5

 

Divide both sides of equation by -2.

 

y = (3/2)x - (5/2)

 

 

To find the y-intercept, set x=0. This is the point on the y-axis.

 

y = (3/2)(0) - (5/2)

y = -5/2

 

The y-intercept is (0, -5/2).

 

 

To find the x-intercept, set substitute y=0. This is the point on the x-axis.

 

0 = (3x - 5) / 2

 

 

zero divided any number is always zero.

 

3x - 5 = 0

3x = 5

  x = 5/3

 

The x-intercept is (5/3, 0).

 

To draw this given line, simply plot the two points on a coordinate system.  Then connect them.  You should get a straight line.