Question

graph the equation
( y = 4x + 2 )
use the graphing tool to graph the line. use the slope and y - intercept when drawing the line.
click to enlarge graph

Explanation:

Step1: Identify slope and y - intercept

The equation of the line is in the slope - intercept form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. For the equation \(y=4x + 2\), the slope \(m = 4\) (which can be written as \(\frac{4}{1}\)) and the y - intercept \(b = 2\). This means the line crosses the y - axis at the point \((0,2)\).

Step2: Plot the y - intercept

On the coordinate plane, find the point \((0,2)\) (since the y - intercept is 2, the x - coordinate is 0 and the y - coordinate is 2) and mark it.

Step3: Use the slope to find another point

The slope \(m=\frac{4}{1}\) means that for a change of \(+ 1\) in the x - value (run), the y - value (rise) changes by \(+4\). Starting from the point \((0,2)\), if we move 1 unit to the right (increase x by 1) to \(x = 1\), we move 4 units up (increase y by 4) from \(y = 2\) to \(y=2 + 4=6\). So we get the point \((1,6)\). We can also move in the opposite direction: for a change of \(- 1\) in x (run left 1 unit) and \(-4\) in y (rise down 4 units) from \((0,2)\), we get the point \((- 1,-2)\).

Step4: Draw the line

Using a straight - edge, draw a line that passes through the points we found (e.g., \((0,2)\) and \((1,6)\) or \((0,2)\) and \((-1,-2)\)). This line represents the graph of the equation \(y = 4x+2\).

Answer:

To graph \(y = 4x + 2\):

1. Plot the y - intercept \((0,2)\).
2. Use the slope \(m = 4=\frac{4}{1}\) to find another point (e.g., from \((0,2)\), move 1 unit right and 4 units up to get \((1,6)\)).
3. Draw a straight line through the plotted points. The line has a positive slope, crosses the y - axis at \((0,2)\), and passes through other points like \((1,6)\), \((-1,-2)\) etc.