Graphing Equations Practice

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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)

Answer 1

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).

1. Finding the Slope (m): The slope formula is:

   \[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

   Using the points (0, 4) and (1, 8):

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

   Plugging in the values:

   \[ m = \frac{8 - 4}{1 - 0} = \frac{4}{1} = 4 \]

2. Finding the Y-intercept (b): The y-intercept is the value of y when x = 0. From the point (0, 4), we can see that b = 4.

3. Writing the Equation: Now that we have the slope (m = 4) and the y-intercept (b = 4), we can write the equation of the line in slope-intercept form:

   \[ y = 4x + 4 \]

So, the equation of the line is y = 4x + 4.