Slope Lesson 2

Slope

VA SOL 7.10

Slope or rate of change, denoted by m, is equal to:

We can find the slope when given a graph by selecting one point and counting how many spaces up or down (rise/vertical) and then how may spaces left or right (run/horizontal) until we reach the second point. 

Ordered Pairs

Always written in the form (x,y)

They tell us WHERE the point is on the coordinate plane.

The x-value tells us to move left or right

The y-value tells us to move up or down

Ordered Pairs (3, 4)

• An ordered pair is a set of coordinates that can be plotted.

• The first number (3) represents movement along the x axis. (horizontal)

• The second number (4) represents movement on the y axis (vertical)

Describing the Graph

• Where it crosses the y-axis is the y-intercept.

• Where it crosses the x-axis is the x-intercept.

• How STEEP it is is called the SLOPE.

y-intercept

• Can be stated TWO WAYS

• ONE: just the number where is crosses the y-axis. In this case -2.

• TWO: the coordinates of where it crosses. In this case (0,-2).

x-intercept

• Can be stated TWO WAYS

• ONE: just the number where is crosses the x-axis. In this case 4.

• TWO: the coordinates of where it crosses. In this case (4,0).

Finding Slope from Ordered Pairs (x,y)

Using a table to generate a line on a graph.

• When you have values for x, simply substitute them into the equation to find values for y.

• If you do not have values for x, you need to make up (or assign) your own values for x.

What is a line?

For our purposes we want to think of a line as a bunch of ordered pairs(dots) in a row. If we plot all the ordered pairs and connect the dots it would form a line. That line would have an infinite amount of ordered pairs, but normally we just look at a few. You only need 2 ordered pairs to see what the line will look like. Draw a line connecting the 2 points and continue the line past the points for the whole line.

Notice in the table, we have 4 ordered pairs listed.

Those 4 ordered pairs are on our line along with a bunch more we did not list. Notice also the equation y=2x+3, this is what a linear(line) equation looks like. It contains one Y variable and one X variable. All linear equations will only contain one X and one Y, or just one Y, or just one X, after combining like terms.

Multiple Choice

Calculate the slope of a line that passes through these points. (1,3)(-1,7)

• -2

• 2

• -5

• -1/2

Multiple Choice

Calculate the slope of a line that passes through these points. (2,0)(7,3)

• 1/3

• 3/5

• 5/3

• 5

Finding Slope from a table:

Choose two coordinates; (x,y). Find the change in y/change in x

Multiple Choice

Calculate the slope of the line:

• 1

• 1/2

• 3

• 3/4

Multiple Choice

Calculate the slope of the line

• 5

• 1/5

• 1/4

• 21

Multiple Choice

Calculate the slope of the line

• -2

• 2

• -1/2

• 1/2

Multiple Choice

Calculate the slope of the line.

• -2/3

• 2/3

• 3/2

• -3/2

Y=MX+B Slope-Intercept Form

This is the most popular way to write a linear equation. Notice the one X and one Y, this represents all the ordered pairs on our line. If we input an X value, you will output one unique Y value(definition of a function) on our line.

The M represents the slope of our line and the B represents the

Y-intercept of our line. Let us examine M and B on the next few slides.

In the formula y=mx+b, m is the slope. This is known as slope-intercept form.

• When slope or m=1, the formula will look like y=x+b.

• When b=0, the formula will look like y=mx.

Multiple Choice

In the equation y=mx+b, what does the m represent?

• slope

• y-intercept

• linear

• point-slope

Multiple Choice

In the equation y=mx+b, what does the m represent?

• slope

• y-intercept

• linear

• point-slope

Multiple Choice

What is the slope for the equation

$$y=x+5$$  ?

• 5

• 1

• 0

• -5

Multiple Choice

What is the slope for the equation

$$y=3x$$  ?

• 3

• 0

• y

• x

• m

Multiple Choice

What is the slope for the equation

$$y=-7x+8$$  ?

• 8

• 8/7

• -7

• 7/8

• 7

Multiple Choice

What is the slope for the equation

$$y=-\frac{4}{3}x+9$$  ?

• $$\frac{3}{4}$$  

• $$\frac{4}{3}$$  

• $$\frac{3}{4}$$  

• $$-\frac{4}{3}$$  

• 9

Multiple Choice

What is the slope for the equation

$$y=\frac{9}{4}x-1$$  ?

• $$\frac{4}{9}$$  

• 1

• $$\frac{9}{4}$$  

• -1