Math  /  Algebra

QuestionA table of values of a linear function is shown below. \begin{tabular}{|c|c|c|c|c|c|} \hlinexx & -1 & 0 & 1 & 2 & 3 \\ \hlineyy & -7 & -8 & -9 & -10 & -11 \\ \hline \end{tabular}
Find the slope and yy-intercept of the function's graph, and find the \begin{tabular}{|ll|} \hline slope: & \square \\ yy-intercept: & \square \\ equation: & \square \\ \hline \end{tabular}

Studdy Solution

STEP 1

What is this asking? We're looking at a straight line disguised as a table, and we need to find its slope, where it crosses the y-axis, and its equation! Watch out! Don't mix up the xx and yy values when calculating the slope!

STEP 2

1. Find the Slope
2. Find the y-intercept
3. Find the Equation

STEP 3

Let's **pick two points** from our table to calculate the slope.
I'm feeling ((-**1**, \)-**7**)) and ((**1**, \)-**9**)).
Remember, slope is the change in yy over the change in xx.

STEP 4

**Calculate the change in** yy: 9(7)=9+7=-9 - (-7) = -9 + 7 = -**2**.
The yy value *decreased* by **2**.

STEP 5

**Calculate the change in** xx: 1(1)=1+1=1 - (-1) = 1 + 1 = **2**.
The xx value *increased* by **2**.

STEP 6

**Divide** the change in yy by the change in xx to find the slope: 22=\frac{-2}{2} = -**1**.
So, our slope is \)-**1**!

STEP 7

The y-intercept is the yy value when x=0x = 0.
Looking at our table, when xx is **0**, yy is \)-**8**.
Boom! Our y-intercept is \)-**8**!

STEP 8

We know the **slope-intercept form** of a linear equation is y=mx+by = mx + b, where mm is the slope and bb is the y-intercept.

STEP 9

We found our **slope** mm is \)-**1** and our **y-intercept** bb is \)-**8**.

STEP 10

**Plug those values** into our equation: y=(1)x+(8)y = (-1)x + (-8), which simplifies to y=x8y = -x - 8.
There's our equation!

STEP 11

Slope: 1-1 Y-intercept: 8-8 Equation: y=x8y = -x - 8

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