QuestionGraph this line using the slope and -intercept:
Click to select points on the graph.
Studdy Solution
STEP 1
What is this asking? We need to draw the line on a graph, using the slope and the -intercept. Watch out! Don't mix up the slope and the -intercept!
STEP 2
1. Find the Slope
2. Find the Y-Intercept
3. Plot the Y-Intercept
4. Use the Slope to Find Another Point
5. Draw the Line
STEP 3
Alright, let's **find the slope**!
Remember, the equation of a line is usually written in the form , where is the **slope**.
Our equation is .
Notice that there's no number explicitly multiplied by , which means it's secretly a **1**!
So, .
This tells us our **slope** is .
STEP 4
Next, let's **find the** -**intercept**!
This is the point where the line crosses the -axis, which happens when .
In our equation, , the -intercept is the value of .
Here, .
So our -intercept is at the point .
STEP 5
Let's **plot** that -**intercept**!
We found it to be , so we'll put a point right there on the graph.
Down six units on the -axis – boom!
STEP 6
Now, let's **use the slope** to find another point!
Our slope is , which can be written as .
Remember, slope is *rise over run*.
So, starting from our -intercept , we'll go up **1** unit (the *rise*) and to the right **1** unit (the *run*).
STEP 7
This lands us at the point .
Let's **plot this new point** on the graph!
STEP 8
Finally, let's **draw our line**!
We've got two points: and .
Connect these points with a straight line, and extend the line in both directions.
Ta-da!
STEP 9
The line for is drawn through the points and .
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