slope and direct variation mr smith. by the end of this you should know what direct variation is,...

Slope and Direct Variation Mr Smith

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Well, what is direct variation?  It’s in the form y=kx, and k=0. we say y varies directly with x, or y is proportionate to x. The k is what relates them, it is the multiplier.  k is the same number all the time, it is constant. And so, it is the same as slope.  When you graph direct variation, notice the x and y-intercepts are both zero. It graphs through the origin.

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Slope and Direct VariationMr Smith

By the end of this… You should know what direct variation is,

why it is important, and how you could use it.

You should know what direct variation and slope have in common.

You should be able to answer questions relating y and x, and use equations in direct variation to your advantage when graphing problems.

Page 3: Slope and Direct Variation Mr Smith. By the end of this You should know what direct variation is, why it is important, and how you could use it

Well, what is direct variation? It’s in the form y=kx, and k=0. we say y

varies directly with x, or y is proportionate to x. The k is what relates them, it is the multiplier.

k is the same number all the time, it is constant. And so, it is the same as slope.

When you graph direct variation, notice the x and y-intercepts are both zero. It graphs through the origin.

Page 4: Slope and Direct Variation Mr Smith. By the end of this You should know what direct variation is, why it is important, and how you could use it

Name the constant (slope) in these 2 problems:

Page 5: Slope and Direct Variation Mr Smith. By the end of this You should know what direct variation is, why it is important, and how you could use it

Name the constant (slope) in these 2 problems:

Page 6: Slope and Direct Variation Mr Smith. By the end of this You should know what direct variation is, why it is important, and how you could use it

These lines can be written as an equation in y = kx form:

y = y = -3x

Page 7: Slope and Direct Variation Mr Smith. By the end of this You should know what direct variation is, why it is important, and how you could use it

Name the constant (slope) in these 2 problems and write the equation of the line:

Page 8: Slope and Direct Variation Mr Smith. By the end of this You should know what direct variation is, why it is important, and how you could use it

The slope is The slope is

y = y = x

Page 9: Slope and Direct Variation Mr Smith. By the end of this You should know what direct variation is, why it is important, and how you could use it

Try working it another way. graph the following. Where would you start?

y = 2x and y =

Page 10: Slope and Direct Variation Mr Smith. By the end of this You should know what direct variation is, why it is important, and how you could use it

Try working it another way. graph the following. Where would you start?

y = 2x and y =

Page 11: Slope and Direct Variation Mr Smith. By the end of this You should know what direct variation is, why it is important, and how you could use it

You can find the constant by knowing what y and x are: If y is 35 when x is

7, what equation could you write? Remember y is the total.

Page 12: Slope and Direct Variation Mr Smith. By the end of this You should know what direct variation is, why it is important, and how you could use it

You can find the constant by knowing what y and x are: If y is 35 when x is

7, what equation could you write? Remember y is the total.

y = kx y = 7x

Now that you have the equation in direct variation form, you can plug in something for x and solve for y.

If x = 6 solve for y.

Page 13: Slope and Direct Variation Mr Smith. By the end of this You should know what direct variation is, why it is important, and how you could use it

You can find the constant by knowing what y and x are: If y is 35 when x is

7, what equation could you write? Remember y is the total.

y = kx y = 7x

Now that you have the equation in direct variation form, you can plug in something for x and solve for y.

If x = 6 solve for y.y = 7xy = 7(6) y = 42

Page 14: Slope and Direct Variation Mr Smith. By the end of this You should know what direct variation is, why it is important, and how you could use it

Try these 2 problems. Write a direct variation equation that relates x and y. then solve. If y = 27 when x =

6, find x when y = 45

If y = 6 when x = , find x when y = 12

Page 15: Slope and Direct Variation Mr Smith. By the end of this You should know what direct variation is, why it is important, and how you could use it

Try these 2 problems. Write a direct variation equation that relates x and y. then solve. If y = 27 when x =

6, find x when y = 45

27 = k(6) y = 4.5x 6 64.5 = k 45 = 4.5x y = 4.5k 4.5 4.5 10 = x

If y = 6 when x = , find x when y = 12

6 = k() y = 9x = k 12 = 9x 9 9 9 = k y = 9x 1.3 = x

Page 16: Slope and Direct Variation Mr Smith. By the end of this You should know what direct variation is, why it is important, and how you could use it

Texbook Problem:

Page 17: Slope and Direct Variation Mr Smith. By the end of this You should know what direct variation is, why it is important, and how you could use it

Textbook Problem:

Here you look what is relating m and e: m= k(e) 60 = k (360) m = 360 360

= k, so m = m = 23 pounds

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