Bot GPT 4-o mini To find the equation of the line in slope-intercept form (y = mx + b), we first need to calculate the slope (m) using the two points provided: (0, -2) and (1, 3).
The formula for the slope (m) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Using the points:
- \((x_1, y_1) = (0, -2)\)
- \((x_2, y_2) = (1, 3)\)
Now, we can plug in the values:
\[ m = \frac{3 - (-2)}{1 - 0} = \frac{3 + 2}{1} = \frac{5}{1} = 5 \]
Now we have the slope \(m = 5\).
Next, we can use one of the points to find the y-intercept (b). The point (0, -2) is particularly useful because the x-value is 0, which directly gives us the y-intercept.
From the point (0, -2):
\[ y = mx + b \quad \text{becomes} \quad -2 = 5(0) + b \] \[ -2 = b \]
Now we have everything we need:
- Slope (m) = 5
- Y-intercept (b) = -2
Putting it all together, the equation of the line in slope-intercept form is:
\[ y = 5x - 2 \]
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