QuestionWrite the equation of the line that passes through the points and . Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.
Answer Attempt 2 out of 2
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Studdy Solution
STEP 1
What is this asking?
We need to find the equation of a line that goes through two given points and write it in point-slope form!
Watch out!
Remember point-slope form is , where is the slope and is a point on the line.
Don't mix up the and coordinates!
STEP 2
1. Calculate the slope
2. Write the equation
STEP 3
Alright, let's **calculate the slope**!
The slope, usually represented by , tells us how steep our line is.
The formula for the slope between two points and is:
Let's label our points.
We'll call as and as .
STEP 4
Now, let's plug the values into our **slope formula**:
Notice how we're subtracting the -values on top and the -values on the bottom.
It's important to keep the order consistent!
STEP 5
Let's simplify:
We can simplify this fraction by dividing both the numerator and the denominator by their **greatest common factor**, which is **2**.
This gives us:
So, our **slope** is .
Awesome!
STEP 6
Now that we have our **slope**, , and we know our line passes through the point , we can use the **point-slope form** of a linear equation:
STEP 7
Let's plug in our **slope** and the point (where and ):
STEP 8
We can simplify the expression inside the parentheses:
And that's our equation in point-slope form!
We could use the other point, , and get an equivalent equation.
STEP 9
The equation of the line in point-slope form is .
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