Direct Variation Slope

Slope-Intercept Form and Direct Variation

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Slope-Intercept Form Notes

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Open Ended

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Open Ended

Write down the notes shown for example 2. Then tell me any questions you have from this example.

Open Ended

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Direct Variation Notes

Copy down the notes shown before moving on to the next slide.

Open Ended

Write down the notes shown for example 1. Then tell me any questions you have from this example.

Open Ended

Write down the notes shown for example 2. Then tell me any questions you have from this example.

Open Ended

Write down the notes shown for example 3. Then tell me any questions you have from this example.

STOP!

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Practice Problems

Answer the questions as best as you can.

Use your notes to help guide you.

Multiple Choice

Write the slope-intercept form of an equation given...

slope is  $$-\frac{1}{3}$$  and y-intercept is $$1$$  

• $$y=-x-\frac{1}{3}$$  

• $$y=-\frac{1}{3}x+1$$  

• $$y=-\frac{1}{3}x-1$$  

• $$y=x-\frac{1}{3}$$  

Multiple Choice

Write the slope-intercept form of an equation given...

a point $$\left(2,-2\right)$$  and a slope = $$-2$$  

• $$y=2x-3$$  

• $$y=2x+2$$  

• $$y=-3x+2$$  

• $$y=-2x+2$$  

Multiple Choice

Write the slope-intercept form of an equation given...

two points $$\left(0,2\right)$$  and  $$\left(4,-2\right)$$  

• $$y=x+2$$  
  

• $$y=-x+2$$  
  

•   $$y=4x+2$$  

• $$y=2x+4$$  
  

Multiple Choice

Write the slope-intercept form of the equation shown in the graph.

• $$y=-3x+1$$

• $$y=x-3$$

• $$y=x+3$$

• $$y=3x+1$$

Multiple Choice

Rewrite the linear equation $$6x+7y=-14$$  into slope-intercept form. 

• $$y=-\frac{4}{7}x-2$$  

• $$y=\frac{6}{7}x-2$$  

• $$y=-2x-\frac{4}{7}$$  

• $$y=-\frac{6}{7}x-2$$  

Multiple Choice

Find the constant of variation for the direct variation.

$$4x=-6y$$  

• $$a=-\frac{2}{3}$$  

• $$a=\frac{2}{3}$$  

• $$a=-\frac{3}{2}$$  

• $$a=-6$$  

Multiple Choice

Find the constant of variation for the table of values shown.

• $$a=-1.5$$  

• $$a=2$$  

• $$a=-0.5$$  

• $$a=-2$$  

Multiple Select

Which linear equations are direct variations? Select all that apply.

• $$y=-8x$$

• $$y-4=3x$$

• $$3y-7=10x$$

• $$4x-3y=0$$

• $$-8y=24x$$

Multiple Choice

The total cost of gasoline varies directly with the number of gallons purchased. Gas costs $1.89 per gallon. Write a direct variation to model the total cost c for g gallons of gas.

• $$g=1.89c$$

• $$c=g+1.89$$

• $$c=1.89g$$

• $$c=\frac{g}{1.89}$$

Multiple Choice

The distance a spring will stretch varies directly with how much weight is attached to the spring. If a spring stretches 9 inches with 100 pounds attached, how far will it stretch with 90 pounds attached? Round to the nearest tenth of an inch.

• $$8.9$$ in.

• $$10$$ in.

• $$8.1$$ in.

• $$9.1$$ in.