Math  /  Algebra

Question5. Which are examples of LINEAR functions? Circle all that apply. x+2y=6x+2 y=6 y=3y=3 x2+y2=4x^{2}+y^{2}=4 y=x2y=x-2 y=12x3y=\frac{1}{2} x^{3} y=12xy=\frac{1}{2} x y=xy=\sqrt{x} \begin{tabular}{|l|l|} \hlineXX & YY \\ \hline 0 & 0 \\ \hline 1 & 1 \\ \hline 2 & 4 \\ \hline 3 & 9 \\ \hline \end{tabular} \begin{tabular}{|c|c|c|c|c|c|} \hlinexx & -2 & -1 & 0 & 1 & 2 \\ \hlineyy & -3 & -1 & 1 & 3 & 5 \\ \hline \end{tabular}
Also... what does a linear graph look like? Don't kunu
6. Which graph best represents the equation 4x+6y=124 x+6 y=12 ? Don A. c. B.
7. A hot air balloon is at an altitude of 400 feet. It begins to descend at a rate of 100 feet per minute. Graph this scenario below.  Identify: 80x+4\text { Identify: } 80 x+4

Slope: \qquad Y-intercept: \qquad 400.

Studdy Solution

STEP 1

What is this asking? We need to figure out which equations or tables show a straight line when graphed, and then describe what a straight line graph looks like. Watch out! Linear functions only involve variables raised to the power of one.
Be careful with squares, cubes, and roots!

STEP 2

1. Identify linear equations
2. Analyze tables for linearity
3. Describe a linear graph

STEP 3

Let's start by looking at each equation and checking if it's linear.
A **linear equation** will have variables only raised to the power of one.
No squares, cubes, or roots allowed!
- x+2y=6x + 2y = 6: Both xx and yy are to the first power. **Linear!** - y=3y = 3: This is a horizontal line, which is a special type of linear equation. **Linear!** - x2+y2=4x^2 + y^2 = 4: Uh-oh, we see squares here. **Not linear!** - y=x2y = x - 2: Both xx and yy are to the first power. **Linear!** - y=12x3y = \frac{1}{2}x^3: The xx is cubed. **Not linear!** - y=12xy = \frac{1}{2}x: Both xx and yy are to the first power. **Linear!** - y=xy = \sqrt{x}: The square root of xx is not linear. **Not linear!**

STEP 4

Now, let's check the tables.
A table represents a linear function if the change in yy is constant for a constant change in xx.
- First table: - xx values: 0, 1, 2, 3 - yy values: 0, 1, 4, 9 - Changes in yy: 10=11 - 0 = 1, 41=34 - 1 = 3, 94=59 - 4 = 5 - The changes aren't consistent. **Not linear!**

STEP 5

- Second table: - xx values: -2, -1, 0, 1, 2 - yy values: -3, -1, 1, 3, 5 - Changes in yy: 1(3)=2-1 - (-3) = 2, 1(1)=21 - (-1) = 2, 31=23 - 1 = 2, 53=25 - 3 = 2 - The changes are consistent. **Linear!**

STEP 6

A **linear graph** is a straight line.
It can be horizontal, vertical, or slanted, but it must be straight.
The line represents a constant rate of change.

STEP 7

The linear functions from the list are: - x+2y=6x + 2y = 6 - y=3y = 3 - y=x2y = x - 2 - y=12xy = \frac{1}{2}x
The second table represents a linear function.
A linear graph looks like a straight line.

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