Math  /  Algebra

Question3. Exit Ticket
Predict how the graphs of the patterns will compare. Explain your thinking. Then complete the tables of values and graph each patte Were your predictions correct? (Knowledge and Understanding) (Thinking) (Commun cation) A: 3x+4-3 x+4 \begin{tabular}{|c|c|} \hlinexx & 3x+4-3 x+4 \\ \hline 0 & 4 \\ \hline 1 & 1 \\ \hline 2 & -2 \\ \hline 3 & -5 \\ \hline \end{tabular} B. 2x+42 x+4 \begin{tabular}{|c|c|} \hlinexx & 2x+42 x+4 \\ \hline 0 & 4 \\ \hline 1 & 6 \\ \hline 2 & \\ \hline 3 & \\ \hline 3 & \\ \hline \end{tabular}

Studdy Solution

STEP 1

What is this asking? We're going to predict, calculate, and then draw how two simple equations, 3x+4 -3x + 4 and 2x+4 2x + 4 , look on a graph! Watch out! Don't mix up your positives and negatives when multiplying!

STEP 2

1. Predict the graphs
2. Complete Table B
3. Graph the lines
4. Check our predictions

STEP 3

Alright, let's look at equation A, y=3x+4y = -3x + 4.
The **slope** is 3-3 and the **y-intercept** is 44.
That means the line starts at 44 on the y-axis and goes *down* as xx gets bigger.

STEP 4

Now, equation B, y=2x+4y = 2x + 4.
The **slope** is 22 and the **y-intercept** is *also* 44.
This line *also* starts at 44 on the y-axis, but it goes *up* as xx increases!

STEP 5

So, both lines meet at (0,4)(0, 4) but go in opposite directions!
One has a negative slope, one has a positive slope.

STEP 6

Table B represents y=2x+4 y = 2x + 4 .
We already have the first two rows.
Let's calculate when x=2 x = 2 .
We substitute x=2x = 2 into the equation: y=22+4=4+4=8 y = 2 \cdot 2 + 4 = 4 + 4 = 8 .
So, when x=2x = 2, y=8y = 8.

STEP 7

Now, let's find yy when x=3x = 3.
Substitute x=3x = 3 into the equation: y=23+4=6+4=10 y = 2 \cdot 3 + 4 = 6 + 4 = 10 .
So when x=3x = 3, y=10y = 10.

STEP 8

We've got all our points!
For equation A, we have (0,4)(0, 4), (1,1)(1, 1), (2,2)(2, -2), and (3,5)(3, -5).
Plot these points and draw a straight line through them.

STEP 9

For equation B, we have (0,4)(0, 4), (1,6)(1, 6), (2,8)(2, 8), and (3,10)(3, 10).
Plot these points and draw a line through them, too.

STEP 10

Do the lines meet at (0,4)(0, 4)?
Do they slope in opposite directions?
If so, our predictions were spot on!

STEP 11

Table B completed:
| xx | 2x+42x + 4 | |---|---| | 0 | 4 | | 1 | 6 | | 2 | **8** | | 3 | **10** |
The graph should show two lines intersecting at (0,4)(0, 4), with line A sloping downwards and line B sloping upwards.

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