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

What is the solution to the following inequality?

$$ 10x-4\leq-3x-8 $$

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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