QuestionA table of values of a linear function is shown below.
\begin{tabular}{|l|l|l|l|l|}
\hline & 0 & 1 & 2 & 3 \\
\hline & 3 & 5 & 7 & 9 \\
\hline
\end{tabular}
Find the slope and -intercept of the function's graph.
slope:
-intercept:
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 (how steep it is) and where it crosses the y-axis.
Watch out!
Don't mix up the and values!
Also, remember that the y-intercept happens when .
STEP 2
1. Find the slope.
2. Find the y-intercept.
STEP 3
The **slope** tells us how much the value changes for every step we take in the direction.
It's like the "rise over run" – how much we go up or down, divided by how much we go sideways.
STEP 4
Let's **pick two points** from our table.
How about and ?
These are great points since they have nice, small numbers.
STEP 5
Now, let's **calculate the rise**.
The value goes from **3** to **5**, so the rise is .
STEP 6
Next, let's **calculate the run**.
The value goes from **0** to **1**, so the run is .
STEP 7
Finally, let's **calculate the slope**.
Remember, it's rise over run!
So, our slope is .
A slope of **2** means that for every step to the right, we go up two steps!
STEP 8
The **y-intercept** is where our line crosses the y-axis.
This happens when .
STEP 9
Look closely at our table!
When , .
That's our y-intercept!
It's as simple as that!
STEP 10
The **slope** of the function is .
The **y-intercept** is .
Was this helpful?