Algebra 1 Common Core Student Edition, Grade 8-9

To w rite a n equation for a direct variation, first find th e co n stan t of variation k using an

ordered pair, o th er th a n (0, 0), th at you know is a solution of th e equation.

Writing a Direct Variation Equation

Suppose y varies directly with x, and y = 35 when x = 5. What direct variation

equation relates x andy? What is the value of y w h en x = 9?

y = kx Start with the function form of a direct variation.

Think 35 = k(5) Substitute 5 for x and 35 for y.

Make sure you d o n 't stop

at 7 = k. To w r i t e t h e 7 = k Divide each side by 5 to solve for k.

direct variation equation, , „ , "V „ y = 7x_ W rite an equation. Substitute 7 for .. .. r , .... t.. k in y = kx..

you have to substitute j /

7 fo r k in y = kx. qhg equation y = 7x relates x and y. When x = 9, y = 7(9), or 63.

Go t I t? 2. Suppose y varies directly with x, and y = 10 w h en x = -2. What direct

variation eq u a tio n relates x an d y? W hat is the value of y w h en x = - 1 5?

Have you graphed
equations like
y = 0.38x before?
Yes. In Chapter 4, you
graphed linear functions
by making a table of
values and plotting
points.^0 0.38(0) = 0

50 0 .3 8 (5 0 ) = 19

100 0.38(100) = 38

150 0.38(150) = 57

Graphing a Direct Variation

Space Exploration Weight on Mars y varies

directly with weight on Earth x. The weights of the

science instruments onboard the Phoenix Mars

Lander on Earth and Mars are shown.

0 What is an equation that relates weight, in

pounds, on Earth x and weight on Marsy?

y = kx S tart w ith the fu n c tio n fo rm o f a d ire c t v a ria tio n.

50 = fc(130) Substitute 130 for x and 50 fo ry.

0.38 ~ k Divide each side by 130 to solve for k.

y = 0.38x Write an equation. Substitute 0.38 for k in y = kx.

The equation y = 0.38x gives th e w e ig h ty on Mars, in

pounds, of an object th at weighs x pounds on Earth.

0 What is the graph of the equation in part (A)?

Make a table of values. Then draw th e graph.

302 Ch ap t er 5 Li n ear Fu n ct i o n s