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Math-John, PhD in Statistics
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Experience:  MS and BS in Math
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# is {(-2,-3), (-1,-2), (2,1), (4,-3)} a linear relation. Why

is {(-2,-3), (-1,-2), (2,1), (4,-3)} a linear relation. Why or why not?
is y=-12x-7 a linear relation. Why or why not?
is f(x)=2x^2=5x a linear relation. Why or why not?

is {(-2,-3), (-1,-2), (2,1), (4,-3)} a linear relation. Why or why not?

No since the first three points are on a straight line but the last one is not on this line. The can be proved by checking the following 3 slopes.

1. Point 1 and 2: (-2-(-3))/(-1 -(-2)) = 1 / 1 = 1,

2. Point 1 and 3: (1 - (-3)) / (2 - (-2)) = 4 / 4 = 1.

The above shows point 1,2,3 are on the same line.

3. Point 1 and 4: (-3-(-3)) / (4-(-2)) = 0.

This shows point 4 is not on the line. The following graph shows this.

is y=-12x-7 a linear relation. Why or why not?

Yes since y is a linear function of x.

is f(x)=2x^2=5x a linear relation. Why or why not?

No since y is a quadratic function of x.

Hope this helps and let me know if you have any questions. Thanks.

John

Customer: replied 5 years ago.
Would these be linear..
*A population of bacteria triples every hour for 4 hours.
*A taxi service charges a \$5 flat fee plus \$2 for each kilometre travelled
1. No, triples means y = c 3^x. It's exponential.

2. Yes since y = 5 + 2x, the fee is linear in mileage.