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.

Question

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

Answer 1

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

1. Find the slope \(m\): The slope \(m\) is calculated using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] We can use the points \((0, 4)\) and \((1, 8)\).

   Here, \((x_1, y_1) = (0, 4)\) and \((x_2, y_2) = (1, 8)\). Plugging in the values, we get: \[ m = \frac{8 - 4}{1 - 0} = \frac{4}{1} = 4 \]

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

   Thus, \(b = 4\).

3. Write the equation of the line: Now that we have the slope and the y-intercept, we can write the equation of the line: \[ y = 4x + 4 \]

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