Problem 66 - Precalculus Essentials

Question

a. Rewrite the given equation in slope-intercept form. b. Give the slope and y-intercept. c. Use the slope and y-intercept to graph the linear function. $$4 y+28=0$$

Step-by-Step Solution

Answer

The slope of the linear function is 0 and the y-intercept is -7. The graph of such a function is a horizontal line crossing the y-axis at -7.

Step 1: Converting to Slope-Intercept form

Firstly, in order to convert the initial equation \(4y + 28 = 0\) into slope-intercept form, isolate y. This can be done by subtracting 28 from both sides and then dividing the result by 4 to free y. This leads to the equation \(y = -7\).

Step 2: Identifying Slope and y-intercept

In the obtained equation, \(y = -7\), it can be observed that it is in the slope-intercept form, where the slope (m) and the y-intercept (b) can be easily identified. In this equation, the term in front of x, which denotes the slope, is absent, indicating a slope of 0. This fact infers that the line is horizontal. Also, -7 acts as the y-intercept (b) which implies that the line intersects the y-axis at point (0, -7).

Step 3: Sketching the Graph

For graphing the function with a slope (m) of 0 and y-intercept (b) at -7, it is noticeable that this line is horizontal and it passes through point (0, -7). Draw a horizontal line at -7 on the y-axis which represents the linear equation graphically.