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Chapter 11: Problem 235

Graph the function \(3 \mathrm{x}-5\).

Short Answer

Expert verified
The function \(y = 3x - 5\) has a slope, \(m = 3\), and a y-intercept, \(b = -5\). First, plot the y-intercept, \((0, -5)\), on the graph. Then, from this point, move one unit to the right and three units up to find the point \((1, -2)\), and continue this pattern to plot the line. Finally, label the line and its key points, such as \((0, -5)\) and \((1, -2)\).

Step by step solution

01

Identify the slope and y-intercept

The given function is in the form \(y = mx + b\), where \(m = 3\) and \(b = -5\). So the slope of the function is 3, and the y-intercept is -5.
02

Plot the y-intercept

The y-intercept is the point where the function crosses the y-axis. In our case, the y-intercept is at the point \((0, -5)\). Mark this point on the graph.
03

Use the slope to draw the line

The slope of the function is 3, which means that for every 1 unit increase in the x-value, the y-value will increase by 3 units. From the y-intercept \((0, -5)\), move one unit to the right and three units up to get another point at \((1, -2)\). Mark this point on the graph and repeat the process to identify more points on the line. Connect the points with a straight line.
04

Label the line and its key points

Label the line as \(y = 3x - 5\). Also, label the y-intercept point as \((0, -5)\) and the point at \((1, -2)\). Providing labels makes it easier to interpret and understand the graph.

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Most popular questions from this chapter

What is the equation of the line through the point \((3,5)\) whose slope is 2 ?

Find the equation of the line which passes through the points \((-3,1)\) and \((7,11)\)

Construct the graph of the function defined by \(\mathrm{y}=3 \mathrm{x}-9\).

Find the equation of the line passing through the points \((2,5)\) and \((6,2)\). Check the results graphically.

Find the point of intersection of the graphs of \(3 \mathrm{x}-\mathrm{y}=5\) and \(9 \mathrm{x}-3 \mathrm{y}=15\)
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