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a graph with (0 , -2) and (1 , 3)

Use the graph to derive the equation of the line in slope intercept form

3 answers

To derive the equation of the line in slope-intercept form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept, we can follow these steps:

  1. Identify the coordinates of the points:

    • Point 1: \((0, -2)\)
    • Point 2: \((1, 3)\)

  2. Calculate the slope (m): The slope \(m\) is calculated using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Substituting the coordinates of the points: \[ m = \frac{3 - (-2)}{1 - 0} = \frac{3 + 2}{1} = \frac{5}{1} = 5 \]

  3. Find the y-intercept (b): Since we have the y-intercept directly from point \((0, -2)\), we know that \(b = -2\).

  4. Write the equation: Now we can substitute \(m\) and \(b\) into the slope-intercept form: \[ y = 5x - 2 \]

Therefore, the equation of the line in slope-intercept form is: \[ y = 5x - 2 \]

you sure

Let's double-check the calculations for the equation of the line given the points \((0, -2)\) and \((1, 3)\).

  1. Identifying Coordinates:

    • Point 1: \((0, -2)\)
    • Point 2: \((1, 3)\)

  2. Calculating the Slope (m): Using the slope formula \(m = \frac{y_2 - y_1}{x_2 - x_1}\):

    • Here, \(y_2 = 3\), \(y_1 = -2\), \(x_2 = 1\), and \(x_1 = 0\). \[ m = \frac{3 - (-2)}{1 - 0} = \frac{3 + 2}{1 - 0} = \frac{5}{1} = 5 \]

  3. Finding the Y-Intercept (b): The y-intercept is the value where the line crosses the y-axis. From the given point \((0, -2)\), we see that: \[ b = -2 \]

  4. Writing the Equation: Now, substituting the values of \(m\) and \(b\) into the slope-intercept form \(y = mx + b\): \[ y = 5x - 2 \]

So, the final equation of the line in slope-intercept form is indeed: \[ y = 5x - 2 \]

The calculation is confirmed to be correct. If you have any specific concerns or follow-up questions, let me know!