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Chapter 3: Problem 67

Use a graphing utility to graph each equation.Then use the \([\text { TRACE }]\) feature to trace along the line and find the coordinates of two points. Use these points to compute the line's slope. $$y=2 x+4$$

Short Answer

Expert verified
The slope of the line represented by the equation \(y = 2x + 4\) is 2. This can be computed using any two points on the line with the formula \(\[m = \frac{y_2 - y_1}{x_2 - x_1}\]\) or can be simply determined from the coefficient of 'x' in the equation.

Step by step solution

01

Graphing the Equation

Firstly, input the equation \(y = 2x + 4\) into a graphing utility. Most graphing calculators or programs have an option to input and graph equations.
02

Finding Two Points on the Line

Once the line has been graphed, use the \(\[TRACE\]\) feature to trace along the line. Note down the coordinates of two distinct points on the line. Let's denote them as \(P(x_1, y_1)\) and \(Q(x_2, y_2)\)
03

Compute the Slope

To find the slope of a line given two points, use the slope formula, which is \(\[m = \frac{y_2 - y_1}{x_2 - x_1}\]\). Here, 'm' is the slope of the line. Substitute the coordinates of the points you recorded into the slope formula.
04

Verify the Slope

Verify the slope from Step 3 is equal to the coefficient of 'x' which is also 2 in the equation \(y = 2x + 4\). This should testify that we have computed the slope correctly.

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Most popular questions from this chapter

Use a graphing utility to graph each equation in Exercises in a standard viewing rectangle, \([-10,10,1]\) by \([-10,10,1] .\) Then use the \([\text { TRACE }]\) feature to trace along the line and find the coordinates of two points. $$y=2 x-1$$

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. I like to select a point represented by one of the intercepts as my checkpoint.

A formula in the form \(y=m x+b\) models the cost, \(y,\) of a four-year college \(x\) years after \(2010 .\) Would you expect \(m\) to be positive, negative, or zero? Explain your answer.

What does it mean if the slope of a line is undefined?

List all the natural numbers in this set: $$ \left\\{-2,0, \frac{1}{2}, 1, \sqrt{3}, \sqrt{4}\right\\} $$ (Section \(1.3,\) Example 5 )
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