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Graphing Equations Practice

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Question
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An illustration of a coordinate plane with four quadrants shows the x-axis ranging from negative 9 to 9 and the y-axis ranging from negative 11 to 11 in increments of 1. A solid upward line with arrows at both ends is plotted on the graph. The line passes through the plotted points left parenthesis 0 comma 4 right parenthesis and left parenthesis 1 comma 8 right parenthesis.

Derive the equation of the line in slope-intercept form.

(1 point)

1 answer

To find the equation of the line in slope-intercept form (y = mx + b), we need to determine the slope \( m \) and the y-intercept \( b \) of the line.

  1. Calculate the slope (m): The slope \( m \) is determined by the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Using the points (0, 4) and (1, 8):

    • \( (x_1, y_1) = (0, 4) \)
    • \( (x_2, y_2) = (1, 8) \)

    Substituting these values into the formula gives: \[ m = \frac{8 - 4}{1 - 0} = \frac{4}{1} = 4 \]

  2. Determine the y-intercept (b): The y-intercept \( b \) is the value of \( y \) when \( x = 0 \). From the point (0, 4), we see that: \[ b = 4 \]

  3. Write the equation: Now that we have \( m = 4 \) and \( b = 4 \), we can write the equation in slope-intercept form: \[ y = 4x + 4 \]

Thus, the equation of the line in slope-intercept form is: \[ \boxed{y = 4x + 4} \]