Expert: Wei Chong - 6/8/2008

Question
Calculate the slope of a line passing through (2,5) with y intercept 3

Answer
Hi Sue,

These are the things that you should understand before you attempt to solve this question:

1) Understand the ideas behind of y-intercept.

The math video in the following link will show you (scroll down to watch the video):

http://www.mathexpression.com/y-intercept.html

2) Understand the Slope Formula

The math video in the following link will show you how to derive and use the Slope Formula:

http://www.mathexpression.com/slope-formula.html


With all these in mind, let's solve your question step-by-step:

1) To calculate the slope using the Slope Formula, we need 2 points.

From the question, we have already been given the point (2,5). We can get the other point using the y-intercept, 3.

2) Y-intercept is actually the y-coordinate of a point on the y-axis

After understanding the ideas behind y-intercept, we should know that y-intercept is actually the y-coordinate of a point on the y-axis.

Also, for any point that lies on the y-axis, the x-coordinate will always be 0.

From this, we have the:

y-intercept = y-coordinate =  3
              x-coordinate = 0

Hence, we have the point (0,3)

3) Use the Slope Formula:

Now that we have 2 points, (2,5) and (0,3). We can use the slope formula:
 
  Slope = (y2 - y1)/(x2 - x1)

Before applying it, we need to assign:

point 1 = (x1,y1) = (2,5)
point 2 = (x2,y2) = (0,3)

Hence, substituting  y2 = 3, y1 = 5, x2 = 0, x1 = 2 into the formula:

Slope = (y2 - y1)/(x2 - x1)
     = (3 - 5)/(0 -2)
     = -2/-2
     = 2/2
     = 1


Hope this helps.

Best Regards,
Wei Chong.