To find the equation of the line that passes through the points (0, 3) and (1, 5), we can follow these steps:
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Find the slope (m): The slope \( m \) of a line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\) is calculated using the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
In our case, we have the points (0, 3) and (1, 5):
\[ m = \frac{5 - 3}{1 - 0} = \frac{2}{1} = 2 \]
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Use the slope-intercept form: The slope-intercept form of the equation of a line is:
\[ y = mx + b \]
where \( m \) is the slope and \( b \) is the y-intercept. We already have \( m = 2 \).
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Determine the y-intercept (b): Since the line passes through the point (0, 3), we can directly see that the y-intercept \( b \) is 3.
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Write the equation: Now we can substitute the values of \( m \) and \( b \) into the slope-intercept form:
\[ y = 2x + 3 \]
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Graph the line: To graph the line \( y = 2x + 3 \):
- Start with the y-intercept (0, 3) on the graph.
- From this point, use the slope \( 2 \) (which means rise over run or 2 units up for every 1 unit right) to find another point. Moving from (0, 3) to (1, 5) confirms that this point is on the line.
- You can plot more points using the slope (for instance, from (1, 5) you would go up 2 to \( y = 7 \) at \( x = 2 \) for another point).
The line will look like:
- A straight line that passes through the points (0, 3) and (1, 5) continuing infinitely in both directions.
The final equation of the line in slope-intercept form is:
\[ \boxed{y = 2x + 3} \]
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