Show:
Identifying Linear Functions
Using Intercepts
Slope
Slope intercept form
Direct variation
100

What is a function whose graph forms a straight line and has a constant change in rate called?

linear function

100
What is the x-coordinate of the point where the graph intersects the x axis called?
What is the x intercept
100
What is the slope of a horizontal line?
Zero
100
What is slope intercept form?
y=mx+b
100

If y varies directly as x and y = 5 when x = 8, find y when x = 9.

K=5/8 

y=45/8


200

What is the standard form of a linear equation?

Ax+By=C

200
Find the x intercept: 2x- 4y=8
x=4
200
What is the slope of a vertical line?
Undefined
200
Write the equation in slope intercept form: slope=0, y intercept =-5
y=-5
200

Example 1: Name the constant of variation for For:

 y = 1/2x ,and the slope.


1/2 and 1/2

300

Tell whether the function is linear and turn it into standard form of linear equation: y=x+3

Yes can be written as -x+y=3

300
Find the x and y intercepts of 3x+4y=24
x=8 and y=6
300
Find the slope of (4,-2) and(-1,2)
What is -4/5
300
Write the equation in slope intercept form: slope=4 and (2,5) is on the line
y=4x-3
300

If y = 4 when x = 2, find y when x = 16.

K=2

y=kx

y=2(16)

y=32

400
Tell whether the set of ordered pairs satisfies a linear function. Explain (2,4), (5,3) (8,2), (11,1)
Yes, constant change in 3 for x. Constant change of -1 in y
400
Find the x and y intercepts of 3x- 2y=12
x=4 and y=-6
400
Find the slope of (20,3000) and (60,2000)
What is -25
400
Graph the equation: y= 4x-3
See graph
400

Direct Variation Problems The distance formula d = rt is a direct variation equation. In the formula, distance d varies directly as time t, and the rate r is the constant of variation.

Use given values for d and t to find r.

        d=rt                    Original equation

     225=r(5)                d=225 miles and t=5 hours

225=r(5)

45=r

45 miles/hour


500

Tell whether the function is linear and graph the function

Yes it is linear.

500
Find the x and y intercepts of 2x + 4y=8. Then graph it
x=4 and y=-2
500
Find the slope of the equation: 6x + 5y=30
What is 6/5
500

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

y=-3/2+4 See graph

500

Charles’s Law states that, at a constant pressure, volume of a gas V varies directly as its temperature T. A volume of 4 cubic feet of a certain gas has a temperature of 200 degrees Kelvin.

A. Write a direct variation equation that relates the variables.

B. Graph the equation on the grid at the right.

C. Find the volume of the same gas at 250 degrees Kelvin.

A. P=T/V