Linear Equations: Intro to Intercepts and Slope

Linear Equations: Intercepts and Slope

Algebra 1

Mrs. LaGrange

Using Intercepts to Graph and Equation:

The x-intercept is the x coordinate where the graph crosses the x-axis. (x, 0)

The y-intercept is the point on the graph where the graph crosses the y-axis. (0, y)

Graphing from Standard Form

Ax + By = C

To graph a linear equation find the intercepts and draw the line that passes through the two intercepts.

*To find x-intercept, let y = 0.

*To find y-intercept, let x = 0.

Multiple Choice

Which ordered pair could represent a y-intercept on a graph?

• (6, 0)
• (0, 4)
• (-1, 3)
• (2, 0)

Multiple Choice

Which ordered pair could represent an x-intercept on a graph?

• (0, 5)

• (0, 4)

• (-1, 3)

• (2, 0)

Multiple Choice

Name the x- and y-intercepts for the equation:
2x + y = 6

• (0, 3) and (6, 0)
• (0, -3) and (-6, 0)
• (3, 0) and (0, 6)
• (-3, 0) and (0, -6)

Multiple Choice

What are the x- and y -intercepts on this graph?

• (0,5), (0,5)
• (5,0), (5,0)
• (5,0), (0,5)
• (0,0), (5,0)

Multiple Choice

Find the x and y intercepts
4x - 5y = 40

• x intercept is 10 
  y intercept is 8
• x intercept is 10
  y intercept is 20
• x intercept is 8
  y intercept is 10
• x intercept is 10
  y intercept is -8

Horizontal and Vertical Lines

When y = c we have a horizontal line that passes through point (0, c) .

When x = c we have a vertical line that passes through point (c, 0).

Multiple Choice

Vertical or horizontal?
y = -3

• vertical 
• horizontal
• neither

Multiple Choice

Vertical or horizontal?
x = 4

• vertical 
• horizontal
• neither

Multiple Choice

Vertical or horizontal?
y = 10

• vertical 
• horizontal
• neither

Multiple Choice

Vertical or horizontal?
x = 1/2

• vertical 
• horizontal
• neither

Multiple Choice

Vertical or horizontal?
y = 2x + 3

• vertical 
• horizontal
• neither

Slope

The slope is the rate of change between any two points on the line.

 $Slope\ =\frac{Rise}{Run}\ =\ \frac{y_2-y_1}{x_2-x_1}$   where  $x_{1\ }\ne\ x_2$  

Multiple Choice

Slope is know as rise/

• run
• fall
• none
• rise

Multiple Choice

Find the slope of the line.

• Undefined
• 0
• 1
• -1

Multiple Choice

Find the slope

• -5/3
• -3/5
• 5/3
• 3/5

Finding slope given two points:

We can find the slope of a line if we are given two points.

 $\left(3,\ 2\right)\ and\ \left(4,\ 6\right)$ 

 $\frac{6-2}{4-3}=\frac{4}{1}=4$   Slope is 4. 

Finding Slope from a table:

Given a table we can choose two points and find the slope of the line.
1.  Choose two points.
2 Use the formula below to find the slope (m).
 $\frac{y_2-y_1}{x_2-x_1}=m$  

Multiple Choice

Find the slope

• -5/3
• -3/5
• 5/3
• 3/5

Multiple Choice

Find the slope of the line.

• 1/4
• -1/4
• -4/1
• 4/1

Multiple Choice

Find the slope:

• 3/4
• 4/3
• -3/4
• -4/3

Multiple Choice

What is the slope?

• 2
• 1/2
• 1
• 1.5

Multiple Choice

What is the slope?

• -1/3
• -3
• -4
• 5

Multiple Choice

What is the slope?

• 1/2
• 2
• 7
• 3

Multiple Choice

Find the slope of the line that passes through:
(6,7) and (4,2)

• 2/5
• -5/2
• 5/2
• -1/2

Multiple Choice

Find the slope of the line that passes through:
(5, -10) and (5, -4)

• undefined
• 0
• - 14/10
• 10/14

Multiple Choice

Find the slope of the line that passes through:
(-4, 7) and (-6, -4)

• 2/11
• 13/2
• 3/10
• 11/2

Summary:

Multiple Choice

Slope is found by counting
_____  ____  _____.

• Rise over Run
• Run over Rise

Multiple Choice

Categorize the slope of the line

• Positive

• Negative

• Zero

• Undefined

Multiple Choice

Categorize the slope of the line

• Positive

• Negative

• Zero

• Undefined

Multiple Choice

Categorize the slope of the line

• Positive

• Negative

• Zero

• Undefined

Multiple Choice

Categorize the slope of the line

• Positive

• Negative

• Zero

• Undefined

Multiple Choice

Categorize the slope of the line

• Positive

• Negative

• Zero

• Undefined