How do i find the slope and y- intersect?

Question

The constant slope of a snow park for boarders can be modeled by the line passing through the point A(3,6) and Point B(7,2). What is the equation of the line that models the terrain of the snow park?

Express your answer in the form y = mx + b.

 

Slope =

Y-intercept =

Equation of the line =

Answer 1

When you have two points the first thing you want to do is to calculate the slope. Remember that the equation for slop is Change in y/Change in x. In other words,  (y₂ -y₁)/ (x₂- x₁).

 

Here is what this equation looks like when I plug in these two given points:

 

(2-6)/ (7-3)

 

After I subtract:

 

-4/4

 

Which simplifies to -1

 

Next to figure out the y intercept I could either graphically solve this problem by drawing in the given points and then adding a -1 slope to find the other points. Remember that a negative slope moves downwards as you move from left to right across the graph paper, and upwards if you move from right to left.

 

Another way to determine the y intercept is to plug in a given point, and then solve for b, since b is the y intercept. That would look like this if I plug in the point (3,6):

 

6= -3 +b

 

I will add -3 to both sides to get the variable by itself

 

9= b

 

 

Now I can plug in my slope and y intercept to write the equation:

 

y= -x + 9

 

 

 

 

Answer 2

Finley did a wonderful job above. :) Nothing I write here should take away from that fact.  I would add a few details to clarify, just in case you're confused.

 

Two points: A(3,6) and Point B(7,2). 

 

Let's call these points (X₁ , Y₁ ) and(X₂ , Y₂).  The formula you may have seen in class for the slope is:

 

Y_{2 -}Y₁

______  = m (the slope)  Just as Finley said, except he omitted the 'm'. 

X₂-X₁

 

So in this case: you have Point A (let's call that Point 1) and Point B (let's call that Point 2).

 

And that means:

 

2-6        -4           -4

___ = _____  =  ____   = -4 = m

7-3       1             1

 

 

The formula for the equation of a line is y= mx +b.  We already know the slope, m = 4.  We need b, the y-intercept.

 

Finley showed you above that b= 9.

 

So now we "plug and chug".  And we have the equation of the line:  y=-4x+9.

 

The equation shows a straight line intersecting the y-axis at (0,9) and having a slope of 9.  This means that the first point to the left (on the negative x side of the y-axis) is (-1,13) and the first point to the right of the y-axis (on the positive x side of the y-axis) is (1, 5).  What is the x-intercept of this line?  You put a zero value for x and you get:

 

0=-4x + 9

 

Bringing the 9 over to the left side by adding -9 to both sides:

 

-9 = -4x

 

Multiplying both sides by -1/4:

 

-9      9

---  = --   =  2 1/4 OR 2.25

-4      4

 

So, the x intercept point is:  (2.25, 0)

 

 

I added the extra details for two reasons: I cried through math because most math teachers are really good at it and omit details.  It is those omission of details that confused me.   I tend to add as many details in math as I can.  

 

In addition, I wanted to attend the Air Force Academy ( I would have been in the 3rd class having female cadets) and at that time the instructors would ask questions far beyond the one given for homework.  So now you have additional information.

 

I hope that you get an 'A' on your homework!

 

Tania