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Chapter 1: Problem 57

Use a graphing utility to graph the equation. Use a standard setting. Approximate any intercepts. $$y=3-\frac{1}{2} x$$

Short Answer

Expert verified
The slope of the line is \(-\frac{1}{2}\), the y-intercept is \(3\), and the x-intercept is approximately \(6\). To get the graph, first plot the y-intercept, then use the slope to find the next points, connect these points to draw the line.

Step by step solution

01

Identify the slope and y-intercept

The slope (m) of the line is \(-\frac{1}{2}\) and the y-intercept (b) is \(3\). These will be useful in plotting the graph.
02

Plot y-intercept

Start by plotting the y-intercept on the y-axis. This is the point \((0, 3)\).
03

Use the slope to find next point

The slope is \(-\frac{1}{2}\), which can be read as 'down 1, right 2'. Starting from the y-intercept point, move down one unit and right two units to get the next point. Repeat this until you have enough points to draw a line.
04

Draw the line

Once enough points are plotted, draw a straight line passing through these points.
05

Find the x-intercept

The x-intercept is where the line crosses the x-axis (i.e, where \(y = 0\)). Substituting \(y=0\) in the given equation, solve for \(x\) to find the x-intercept.
06

Approximate the intercepts

Intercepts are integral points where the line crosses the axes. By analysing our graph, we can estimate these points.

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