Bot GPT 4-o mini To find the equation of the line that passes through the points (0, -3) and (3, 0), we can use the slope-intercept form of the equation of a line, which is given by:
\[ y = mx + b \]
where \( m \) is the slope and \( b \) is the y-intercept.
Step 1: Calculate the slope (m)
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 (0, -3) \((x_1, y_1)\) and (3, 0) \((x_2, y_2)\):
\[ m = \frac{0 - (-3)}{3 - 0} = \frac{3}{3} = 1 \]
Step 2: Determine the y-intercept (b)
The y-intercept \( b \) is the y-coordinate of the point where the line crosses the y-axis, which is the \( y \)-coordinate when \( x = 0 \). From the point (0, -3), we can see that:
\[ b = -3 \]
Step 3: Write the equation of the line
Now that we have the slope and y-intercept, we can write the equation of the line:
\[ y = 1x - 3 \quad \text{or simply} \quad y = x - 3 \]
Summary
- The y-intercept of the line is \( -3 \).
- The equation of the line is \( y = x - 3 \).
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