SLOPE AND Y-INTERCEPTMarch 24, 2011

What is slope?

The slope of a line is the ratio that describes its tilt.

The slope of a line can be:

Positive Negative

What is slope?

Zero Undefined

How do we find the slope?

1. Find two points on the line with coordinates that are easy to read.

How do we find the slope?

2. Between these two points, find the rise (the change in y going up or down) and the run(the change in x going left or right) .

Run= 4

Rise=3

How do we find the slope?

3. To find the slope, divide the rise by the run.

Run= 4

Rise=3

STOP

Now, work problems 1 and 2 on the Reteaching 8-3 worksheet.

Answer to #1: -3

Answer to #2: -5/2

Another way to find the slope

We can also find the slope using only the coordinates of the two points.

Suppose we have points A (4,5) and B (0,2).

To find the slope, find the difference between the y-coordinates of A and B (the rise) and divide it by the difference between the x-coordinates (the run).

STOP

Now, work problems 3 and 6 on the Reteaching 8-3 worksheet.

Answer to #3: 1/4

Answer to #6: 3

Finding the equation of a line

Now that we know the slope of our line, we can find its equation using slope-intercept form.

But before we can do this, we must find the y-intercept of the line.

Y-intercept= the value of y when x is zero

Finding the equation of a line

To find the y-intercept, follow the y-axis upward or downward until you reach the line.

Y-intercept = 2

Finding the equation of a line

Now that we know the slope and y-intercept, we use this equation:

y = mx + b where m is the slope and b is the y-

intercept.Since our slope was m=3/4 and our y-

intercept was b=2, the equation of our line is:

y= ¾ x + 2.

STOP

Now, work problem #1 on the Practice 8-4 worksheet.

Answer to #1: y = -5/4 x + 2

Graphing Linear Equations

Now that we know y= mx + b, we can graph linear equations much more easily.

Let’s try the equation: y= 2/3 x + 1

1. Identify m(slope) and b(y-intercept).

In this case, m= 2/3 and b= 1.

Graphing Linear Equations

2. Place a point at (0, b). An easy way to remember this is that b is for begin. In this case, that would be the point (0,1).

Graphing Linear Equations

3. Now, use the slope to plot another point. We know that our slope is 2/3, so we want to go up 2 units and 3 units to the right.

Graphing Linear Equations

4. Next, connect the two points with a ruler or straightedge, extending the line in both directions.

STOP

Work problem 9 on the Practice 8-3 worksheet.

Answer to #9:

Writing a Linear Equation from a Table

Suppose you are given a table like this:

x y

-2 -11

0 -5

2 1

4 7

Writing a Linear Equation from a Table

1. First, look for a pattern on each side of the table. For this table, we notice:

x y

-2 -11

0 -5

2 1

4 7

+6

+6

+6

+2

+2

+2

Writing a Linear Equation from a Table

2. Next, divide the change in y by the change in x to get the slope. In this case,

3. To find the y-intercept, we simply look at the table and find the value of y when x=0. In this case, y= -5.

Writing a Linear Equation from a Table

4. Now that we have m=3 and b= -5, we can plug these values into y= mx + b to get our equation.

So we have y= 3x – 5.

STOP

Now, work problems 1 and 2 from the Reteaching 8-4 worksheet.

Answer to #1: y= 7x

Answer to #2: y= x - 8

THE END

Have a wonderful day!