Find the Line Equation: Points (-2,3) and (0,1)

Q: What does a negative slope mean?

A negative slope means the line goes downward from left to right. In this case, m = -1 means for every 1 unit you move right, the line drops down 1 unit.

Q: How do I handle negative coordinates in the formula?

Be extra careful with negative signs! Remember that subtracting a negative number becomes addition: 0 - (-2) = 0 + 2 = 2.

Q: Can I check my slope answer?

Yes! Count the rise and run on a graph. From (-2,3) to (0,1): move right 2 units, down 2 units. So slope = $ \frac{-2}{2} = -1 $ ✓

Q: What if I get a fraction that doesn't simplify to a whole number?

That's perfectly normal! Many slopes are fractions like $ \frac{2}{3} $ or $ \frac{-5}{4} $. Just make sure to simplify the fraction to lowest terms.

Slope Formula with Coordinate Points

The line passes through the points $(-2,3),(0,1)$

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Step-by-step video solution

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00:00 Find the slope of the graph

00:05 For each point, we'll mark X and Y

00:13 We'll use the formula to find the slope using 2 points on the graph

00:22 We'll substitute appropriate values according to the given data, and solve to find the slope

00:41 And this is the solution to the question

Step-by-step written solution

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Understand the problem

The line passes through the points $(-2,3),(0,1)$

Step-by-step solution

To find the slope of the line passing through the points $(-2, 3)$ and $(0, 1)$ , we use the formula for the slope $m$ between two points $(x_1, y_1)$ and $(x_2, y_2)$ :

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Substituting the given points $(x_1, y_1) = (-2, 3)$ and $(x_2, y_2) = (0, 1)$ , we have:

$m = \frac{1 - 3}{0 - (-2)}$

This simplifies to:

$m = \frac{-2}{2}$

So, the slope is:

$m = -1$

Thus, the slope of the line is $-1$ , corresponding to choice 2.

Final Answer

$m=-1$

Key Points to Remember

Essential concepts to master this topic

Formula: Use m = (y₂ - y₁)/(x₂ - x₁) for slope between points
Technique: Substitute (-2,3) and (0,1): m = (1-3)/(0-(-2)) = -2/2
Check: Rise = -2, run = 2, so slope = -2/2 = -1 ✓

Common Mistakes

Avoid these frequent errors

Mixing up the coordinate order
Don't use (y₁ - y₂)/(x₁ - x₂) instead of (y₂ - y₁)/(x₂ - x₁) = wrong sign! This flips the slope direction and gives the opposite answer. Always keep the same order: subtract first point from second point in both numerator and denominator.

Practice Quiz

Test your knowledge with interactive questions

Look at the linear function represented in the diagram.

When is the function positive?

FAQ

Everything you need to know about this question

Which point should I call (x₁, y₁) and which should be (x₂, y₂)?

It doesn't matter which point you choose as first or second! Just make sure you're consistent - if (-2,3) is your first point, then (0,1) must be your second point throughout the calculation.

What does a negative slope mean?

A negative slope means the line goes downward from left to right. In this case, m = -1 means for every 1 unit you move right, the line drops down 1 unit.

How do I handle negative coordinates in the formula?

Be extra careful with negative signs! Remember that subtracting a negative number becomes addition: 0 - (-2) = 0 + 2 = 2.

Can I check my slope answer?

Yes! Count the rise and run on a graph. From (-2,3) to (0,1): move right 2 units, down 2 units. So slope = $\frac{-2}{2} = -1$ ✓

What if I get a fraction that doesn't simplify to a whole number?

That's perfectly normal! Many slopes are fractions like $\frac{2}{3}$ or $\frac{-5}{4}$ . Just make sure to simplify the fraction to lowest terms.

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