To graph an equation in the form y=kx:

* Plot a point at the origin (0,0)* Use the slope (rise/run) to find the next point* Connect points with a line

Direct Variation

y = kx

(y=mx is the same)

3-4 Direct Variation

Direct variation - when two variables relate to one another only by a constant. We say they are directly proportional. The constant is the same as slope, and we call it the constant of variation, k. Yes, m and k are the same.

Ex. 1C ! Name the constant of variation:

Find the slope of the line using the points:

(Look at examples 1 a and b in the book if you need more.)

Notice that no matter what k is, all direct variation equations will pass through the _____________. Because subbing 0 for x will always give a y value of 0 as well.

This makes graphing a direct variation equation super easy.

Ex. 2B! ! ! ! ! ! ! Ex. 2C

!

They = 2

3x!! ! ! ! ! ! y = !5x

(3-4)

y = 2.1x

(0,0)(1,2.1)

Ex. 3CYP Suppose y varies directly as x, and y = 98 when x = 14. Write a direct variation equation that relates x and y. Then find y when x = -4. (follow the above steps)

Ex. 3C Suppose y varies directly as x, and y = 9 when x = -3. Write a direct variation equation that relates x and y. Use the direct variation equation to find x when = 15.

(3-4)

To write and solve a direct variation equation:

* The problem will say ‘y varies directly as x’ or ‘distance varies directly with time’...this phrasing is how you know to use the general direct variation equation.* Start by writing y = kx.* You will be given one x & y pair. Use this to find the constant of

variation k for the equation.* Plug in the given x & y pair and solve for k.* Now start over with the general equation y=kx, but

substitute your new k value. (x and y will still be variables!)* Use this equation to solve the question being asked.

y = -3x, x = -5

Ex. 4CYP A hot-air balloonʼs height varies directly as the balloonʼs ascent time in minutes. Write a direct variation for the distance d ascended in time t. Graph the equation. Estimate how many minutes it would take to ascent 2100 feet. About how many minutes would it take to ascend 3500 feet?

Ex. 4E The Ramirez family is driving cross-country on vacation. They drive 330 miles in 5.5 hours. Write a direct variation equation to find the distance d driven in time t. Graph the equation. Estimate how many hours it would take to drive 500 miles.

Biblical Integration:

Graphing helps reveal creation. Remember that equations describe relationships in sets of data, and graphs are a visual representation of those relationships. The slope of the graphed line quickly reveals to us the severity of that relationship, if it is a direct relationship. Seeing the relationship between parts of God's creation helps us understand and sometimes interact with it.

Problems for Practice: 13, 17, 33, 43 (reduced from video) Complete on notebook paper or the back of these printed notes, in notes section of binder. Check with the back of the book. Place a colored check by correct answers. Correct incorrect answers to the right. Use Hotmath if you need help.

Also complete the following Spiral Review: 63

(3-4)

d=60t, , about 8.3 h