Practice finding slope by connecting points on this coordinate plane grid

Let’s solve this step by step.

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Step 1: Identify the two points on the graph

Looking at the image, we see two red dots:

- One point is at (–2, –2) — that’s 2 units left and 2 units down from the origin.
- The other point is at (5, 3) — that’s 5 units right and 3 units up from the origin.

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Step 2: Use a ruler to connect the points

This is just a visual instruction — you’re supposed to draw a straight line between (–2, –2) and (5, 3). This line represents the linear relationship between these two points.

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Step 3: Determine if the slope is positive, negative, or undefined

Slope tells us how steep the line is and in which direction it goes.

- If the line goes uphill from left to right → positive slope
- If the line goes downhill from left to right → negative slope
- If the line is horizontal → slope = 0
- If the line is vertical → slope is undefined

In our case, going from (–2, –2) to (5, 3), we move right and up, so the line slopes upward → positive slope

✔ So, “This slope is positive.”

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Step 4: Fill in the blanks for rise and run

We’re asked:

> To get from the point (_____) to point (_____), you must rise ___ and run ___.

You can go from left to right — so from the leftmost point to the rightmost point:

→ From (–2, –2) to (5, 3)

Now calculate:

- Rise = change in y = y₂ – y₁ = 3 – (–2) = 5
- Run = change in x = x₂ – x₁ = 5 – (–2) = 7

✔ So:

> To get from the point (–2, –2) to point (5, 3), you must rise 5 and run 7.

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Step 5: Calculate the slope

Slope (m) = rise / run = 5 / 7

✔ So, “The slope is: 5/7”

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## ✔ Final Answers:

- This slope is positive.
- To get from the point (–2, –2) to point (5, 3), you must rise 5 and run 7.
- The slope is: 5/7

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💡 Extra Tip:

You can also write the slope as a decimal (~0.714), but unless asked, fractions are preferred in math problems like this because they’re exact.

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Let me know if you’d like to see the graph drawn or the equation of the line too!