Consider the three points (-4,-3) , (20,15) , and (48,36).

Part AWhich points are on the same line that passes through (-4,-3) , (20,15) , and (48,36)? Select all that apply. A.) (-8,-6) B.) (-2,-1) C.) (0,0) D.) (4,3) E.) (6,8) Part CDo the points on the line y = 3x - 2 have a constant ratio of the y-coordinate to the x-coordinate for any point on the line except for the y-intercept? Explain your answer. |
Part BUse the information from Part A to explain why the ratio of the y-coordinate to the x-coordinate is the same for any point on the line except the y-intercept. Explain why this is not true for the y-intercept. |

__Part A__The model for direct variation is y = kx

k = y/x {divided each side by x}

If a point is on the same line, it should have

the same y/x ratio, equaling the constant of variation, k.

For the first point (-4,-3), the constant of variation is:

k = (-3) / (-4) = 3/4 {reduced the constant of variation}

The points that have a y/x ratio of 3/4 are:

**A.) (-8,-6)**

and

**D.) (4,3)**

__Part B__In part A, the constant of variation, k = y/x , was found to be 3/4 .

Every point on the line has a ratio of the y-coordinates to the x-coordinates being 3/4,

except the y-intercept.

At the y-intercept, the value of x is 0. Therefore, if x is zero, then k=y/x would be undefined.

__Part C__No. The equation y = 3x – 2 is not in the form of direct variation, which is y = kx, because

of the constant term, -2.

Example:If x = 2 y = 3(2) – 2 {substituted 2 for x} y = 6 – 2 {multiplied} y = 4 {subtracted} (2 , 4) {the coordinates on the line} The ratio of the y-coordinate to the x-coordinate would be 4/2 = 2 |
Example:If x = 5 y = 3(5) – 2 {substituted 5 for x} y = 15 – 2 {multiplied} y = 13 {subtracted} (5 , 13) {the coordinates on the line} The ratio of the y-coordinate to the x-coordinate would be 13/5. |

Therefore, the ratio of the y-coordinate to the x-coordinate is

**constant.**__not__

*- Algebra House*