Linear Functions

Identifying Linear Functions

100

What is a function whose graph forms a straight line called?

linear function

200

What is the standard form of a linear equation?

Ax+By=C

300

How can you determine the slope and the y-intercept of a line from a graph?

Find the slope of the line using the coordinates of two points found on the graph. Then find the y coordinate of the point where the graph crosses the y-axis.

400

Explain if the equation is a linear equation.

                    y=x² -1

No, the equation can not be written in the form

 y = mx + b and the graph of the solution is not a line.

500

Explain how you can use a table of values, an equation, and a graph to determine whether a function represents a proportional relationship.

A table of values will include (0,0) and show a constant rate of change. An equation will be of the form y=mx 

A graph will be a line passing through the origin.

Using Intercepts

100

What is the x-coordinate of the point where the graph intersects the x axis called?

What is the x intercept

200

Find the x intercept: 2x- 4y=8

x=4

300

Find the x and y intercepts of 3x+4y=24

x=8 and y=6

400

Find the x and y intercepts of 3x- 2y=12

x=4 and y=-6

500

Find the x and y intercepts of 2x + 4y=8. Then graph it

x=4 and y=-2

Slope

100

What is the slope of a horizontal line?

Zero

200

What is the slope of a vertical line?

Undefined

300

Find the slope of (4,-2) and(-1,2)

What is -4/5

400

Find the slope of (20,3000) and (60,2000)

What is -25

500

Find the slope of the equation: 6x + 5y=30

What is -6/5

Slope intercept form

100

What is slope intercept form?

y=mx+b

200

Write the equation in slope intercept form: slope=0, y intercept =-5

y=-5

300

Write the equation in slope intercept form: slope=4 and (2,5) is on the line

y=4x-3

400

Graph the equation: y= 4x-3

See graph

500

Write the equation in slope intercept form and graph: 3x+2y=8

y=-3/2+4 See graph

Point Slope form &Slopes of lines

100

Write the linear equation in point slope form: Slope=-7 ; (4,2)

y-2 = -7(x -4)

200

What lines have the same slope?

parallel

300

How do you know when you have perpendicular slopes?

When the product of the slopes equal -1

400

Write this equation in point slope form & in slope intercept form: slope=-4, (-1,-2)

Point slope form: y+2= -4(x+1) Slope intercept: y=-4x -6

500

Write the equation in point slope form and in slope intercept form: (1,-4) and (3,2)

Point slope: y-2=3 (x-3) slope intercept: y=3x -7