8th grade math review Slope and Equations

8th grade math review Slope and Equations

Coordinate Plan

• A coordinate plane as 2 axis.

• The x axis moves from left to right (horizontal)

• The y axis moves up and down (vertical)

Multiple Choice

How many axis are on a coordinate plane?

• 1

• 2

• 3

Multiple Choice

Which axis moves in a vertical direction?

• x

• y

• z

Multiple Choice

Which axis moves in a horizontal direction?

• x

• y

• z

Quadrants

• A coordinate plane has 4 quadrants.

• The quadrants are named quadrant 1, 2, 3, and 4.

• Starting in the upper right hand corner is quadrant 1, and you move in a counter clockwise direction when counting them off.

Multiple Choice

When counting quadrants, we start in the upper right hand corner and move in what direction?

• Clockwise

• counterclockwise

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)

Graphing Linear Equations

• We can use an equation to graph a line. When we use an equation to graph a line, we call that a linear equation.

• y=-2x+1

• 
  

Ex. y=-2x+1. x=1

• To solve this equation you would need to substitute the value of 1 in for x.

• The value that you get for y= would be your coordinate value for y in your (x,y) ordered pair.

• If x=1, then y=-2(1)+1

• (-2)1=-2

• -2+1=-1

• y=-1

• x=1, y=-1 (1, -1)

Multiple Choice

Solve the equation for y using x=0

Y=-2x+1

• -1

• 0

• 1

Multiple Choice

In the previous example where x=0, what would our ordered pair be?

• (0, -1)

• (0,1)

• (1,0)

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.

Multiple Choice

When you are asked to graph a line using a table, but you do not have any values for x, what do you do?

• Sit there confused doing nothing too shy to ask for help?

• Wait for the teacher to tell you what to do?

• Assign (make up) your own values for x, substitute them into the equation and solve for y?

Open Ended

Use the table shown to find values for y in the equation y=3x-1.

Use x=1 and x=2.

You should have two values for y. y=? and y=?

Slope

• Slope is the rate of change between any 2 points on a line. It is a measure of steepness of the line.

• To find the slope of a line we need to find the ratio of the change in y (vertical change) to the change in x (horizontal change).

• Remember to move like pac-man.

• Rise over run

Slope Formula

•  $slope=\frac{Y_2}{x_2-}\frac{-Y_1}{x_1}$  

• In order to find slope using slope formula you will need 2 sets of ordered pairs.

• Assign one set your X1 and Y1, and the other set your Y1 and Y2

Examples

• In the example we have 2 sets of ordered pairs. (-3,-1) and (3,4)

• We chose for our X1,Y1, (-3,-1) for X2,Y2 we chose (3,4)

• When we substitute our values into our formula we get

   $\frac{5}{6}$  

Positive and Negative slopes

• Positive Slope, the line rises from left to right.

• Negative Slope, the line falls from left to right.

Multiple Choice

Estimate if the slope of this line would be positive or negative?

• positive

• negative

Multiple Choice

Estimate if the slope of this line would be positive or negative?

• positive

• negative

Finding the slope of a horizontal line

• If you substitue the values from our ordered pairs into the equation for slope formula

• You would get

   $\frac{0}{7}$  

• The slope of this line would be zero.

• Horizontal lines have a slope of zero because their is no change along the y axis.

Multiple Choice

The slope of a horizontal line is?

• positive

• negative

• 0

• undefined

Finding the slope of a vertical line

• If you substitute the values for our coordinates into the equation for slope formula.

• You would get  $\frac{4}{0}$  

• We cannot divide a number by zero. So the slope is undefined, because we cannot define it.

• Vertical lines have a slop of undefined

Multiple Choice

The slope of a vertical line is?

• positive

• negative

• 0

• undefined