QuestionEx. 4 Graph
Studdy Solution
STEP 1
What is this asking?
We need to graph all the points that make the inequality true!
Watch out!
Remember that the line is *not* part of the solution because we're dealing with a "less than" sign, not a "less than or equal to" sign.
We'll represent this on the graph with a **dashed line**.
STEP 2
1. Rewrite the inequality as a linear equation.
2. Find two points that satisfy the equation.
3. Graph the line represented by the equation.
4. Determine which side of the line represents the solution to the inequality.
STEP 3
Let's change the inequality to the equation .
This equation represents the **boundary line** of our inequality.
STEP 4
To graph the line, we need at least two points.
A super easy point to find is the **x-intercept**!
To find it, we set in our equation .
This gives us , which simplifies to .
Dividing both sides by gives us , which is the same as .
So, our first point is .
STEP 5
Now, let's find the **y-intercept**!
This time, we set in our equation .
This gives us , which simplifies to .
Dividing both sides by gives us .
So, our second point is .
STEP 6
Now, we'll **plot** the two points and on a coordinate plane.
Remember, since our original inequality was , we'll draw a **dashed line** through these points.
The dashed line indicates that the points on the line are *not* included in the solution.
STEP 7
The line divides the plane into two regions.
We need to figure out which side satisfies the inequality.
The easiest way to do this is to **test a point**!
Let's pick the origin because it's simple to work with.
STEP 8
Substitute and into the inequality .
This gives us , which simplifies to .
This is **true**!
STEP 9
Since makes the inequality true, the region containing the origin is our solution.
We **shade** this region to indicate all the points that satisfy the inequality .
STEP 10
The solution is the shaded region below the dashed line passing through the points and .
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