Calculate Slope Between Points (0,4) and (-5,6): Coordinate-Based Problem

Q: Why is my slope negative when the line seems to go up?

Remember that slope depends on direction! Moving from (0, 4) to (-5, 6) means going left and up. Since we move left (negative x-direction), the slope is negative even though y increases.

Q: Does it matter which point I call (x₁, y₁)?

No! You can choose either point as your starting point. Just be consistent - if (0, 4) is (x₁, y₁), then (-5, 6) must be (x₂, y₂). You'll get the same slope either way.

Q: How do I handle the negative signs correctly?

Be extra careful with subtraction! When you see $ x_2 - x_1 = -5 - 0 = -5 $, remember that subtracting zero doesn't change the sign. The negative comes from the coordinate itself.

Q: What does a slope of -2/5 actually mean?

It means for every 5 units you move right, the line drops 2 units down. Or for every 5 units left, it rises 2 units up. The negative tells you the line is decreasing overall.

Slope Formula with Negative Coordinates

What is the slope of a straight line that passed through the points $(0,4),(-5,6)$ ?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:07 Let's find the slope of the graph.

00:11 We will calculate it using two points.

00:18 Here's the formula for finding the slope using two points.

00:28 We'll plug in the right numbers from our data to solve for the slop e.

00:49 This gives us the slope of the graph.

00:53 And that's how we solve the problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

What is the slope of a straight line that passed through the points $(0,4),(-5,6)$ ?

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Identify the given information about the points.
Step 2: Use the slope formula to find the slope.
Step 3: Calculate and simplify.

Now, let's compute the slope:

Step 1: The points given are $(0, 4)$ and $(-5, 6)$ .

Step 2: Apply the slope formula:

The slope $m$ is given by:

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

Substitute the known values:

y_2 = 6, \; y_1 = 4, \; x_2 = -5, \; x_1 = 0

m = \frac{6 - 4}{-5 - 0} = \frac{2}{-5}

Step 3: Simplify the expression:

m = -\frac{2}{5}

Thus, the slope of the line passing through the points $(0, 4)$ and $(-5, 6)$ is $-\frac{2}{5}$ .

Therefore, the solution to the problem is $-\frac{2}{5}$ .

Final Answer

$-\frac{2}{5}$

Key Points to Remember

Essential concepts to master this topic

Formula: Slope equals rise over run: $m = \frac{y_2 - y_1}{x_2 - x_1}$
Technique: Substitute carefully: $\frac{6-4}{-5-0} = \frac{2}{-5} = -\frac{2}{5}$
Check: Verify by plotting points and counting rise/run visually ✓

Common Mistakes

Avoid these frequent errors

Mixing up coordinate order when subtracting
Don't randomly subtract coordinates like (6-0) ÷ (4-(-5)) = wrong answer! This mixes up x and y values from different points. Always keep coordinates organized: use (x₁, y₁) = (0, 4) and (x₂, y₂) = (-5, 6) consistently in the formula.

Practice Quiz

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For the function in front of you, the slope is?

FAQ

Everything you need to know about this question

Why is my slope negative when the line seems to go up?

Remember that slope depends on direction! Moving from (0, 4) to (-5, 6) means going left and up. Since we move left (negative x-direction), the slope is negative even though y increases.

Does it matter which point I call (x₁, y₁)?

No! You can choose either point as your starting point. Just be consistent - if (0, 4) is (x₁, y₁), then (-5, 6) must be (x₂, y₂). You'll get the same slope either way.

How do I handle the negative signs correctly?

Be extra careful with subtraction! When you see $x_2 - x_1 = -5 - 0 = -5$ , remember that subtracting zero doesn't change the sign. The negative comes from the coordinate itself.

What does a slope of -2/5 actually mean?

It means for every 5 units you move right, the line drops 2 units down. Or for every 5 units left, it rises 2 units up. The negative tells you the line is decreasing overall.

Can I simplify -2/5 further?

No - this fraction is already in its simplest form! Since 2 and 5 share no common factors other than 1, $-\frac{2}{5}$ cannot be reduced further.

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