Finding the Slope: Right Triangle Formed by (5,0) and (0,-5)

Q: Why do we get a positive slope when both coordinates change signs?

Great observation! When we calculate $ \frac{-5-0}{0-5} = \frac{-5}{-5} $, we have negative divided by negative, which always equals positive. The line goes up from left to right!

Q: How can I remember the slope formula correctly?

Think "rise over run": $ m = \frac{\text{rise}}{\text{run}} = \frac{y_2-y_1}{x_2-x_1} $. The y-values (vertical change) go on top, x-values (horizontal change) go on bottom.

Q: Can I use either point as point 1 or point 2?

Yes! As long as you keep coordinates together as pairs. Using (0,-5) first gives $ \frac{0-(-5)}{5-0} = \frac{5}{5} = 1 $ - same answer!

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

That's completely normal! Many slopes are fractions like $ \frac{2}{3} $ or $ -\frac{1}{4} $. Just make sure your fraction is in lowest terms.

Slope Calculation with Coordinate Points

Calculate the slope of the line that forms a right triangle with the axis x and the axis y and passes through the points $(5,0),\lparen0,-5)$ .

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the slope of the line

00:03 We will use the formula to find the slope of a line using 2 points

00:08 We will substitute the points according to the given data and solve for the slope

00:30 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Calculate the slope of the line that forms a right triangle with the axis x and the axis y and passes through the points $(5,0),\lparen0,-5)$ .

Step-by-step solution

To solve this problem, we will calculate the slope of the line passing through the given points:

Step 1: Identify coordinates: The points are $(5, 0)$ and $(0, -5)$ .
Step 2: Use the slope formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Substituting the coordinates, we have: $m = \frac{-5 - 0}{0 - 5}$
Step 3: Simplify the expression: $m = \frac{-5}{-5} = 1$

Thus, the slope of the line is $1$ .

Therefore, the solution to the problem is $1$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Slope Formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$ for any two points
Technique: Substitute $\frac{-5 - 0}{0 - 5} = \frac{-5}{-5} = 1$
Check: Negative divided by negative equals positive; verify coordinates match line equation ✓

Common Mistakes

Avoid these frequent errors

Mixing up coordinate order in slope formula
Don't randomly assign coordinates to $x_1, y_1$ and $x_2, y_2$ = wrong slope! Mixing (5,0) and (0,-5) incorrectly gives $\frac{0-(-5)}{5-0} = 1$ by luck, but usually produces errors. Always keep coordinates as pairs: if (5,0) is point 1, then $x_1=5, y_1=0$ .

Practice Quiz

Test your knowledge with interactive questions

Which statement best describes the graph below?

FAQ

Everything you need to know about this question

Why do we get a positive slope when both coordinates change signs?

Great observation! When we calculate $\frac{-5-0}{0-5} = \frac{-5}{-5}$ , we have negative divided by negative, which always equals positive. The line goes up from left to right!

What does it mean that this line forms a right triangle with the axes?

The line connects (5,0) on the x-axis to (0,-5) on the y-axis, creating a right triangle with the origin (0,0). The legs have lengths 5 and 5, making it an isosceles right triangle!

How can I remember the slope formula correctly?

Think "rise over run": $m = \frac{\text{rise}}{\text{run}} = \frac{y_2-y_1}{x_2-x_1}$ . The y-values (vertical change) go on top, x-values (horizontal change) go on bottom.

Can I use either point as point 1 or point 2?

Yes! As long as you keep coordinates together as pairs. Using (0,-5) first gives $\frac{0-(-5)}{5-0} = \frac{5}{5} = 1$ - same answer!

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

That's completely normal! Many slopes are fractions like $\frac{2}{3}$ or $-\frac{1}{4}$ . Just make sure your fraction is in lowest terms.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Linear Functions questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime