Problem 67 - Introductory and Intermediate Algebra for College Students 4th

Question

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. $$y=2 x+4$$

Step-by-Step Solution

Answer

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 1: 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.

Step 2: 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 \(Q(x_2, y_2)\)

Step 3: 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.

Step 4: 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.