Question

graph the line that has a slope of 4 and includes the point (0, 2). click to select points on the graph.

Explanation:

Step1: Identify the y-intercept

The point \((0, 2)\) is on the y - axis (since \(x = 0\)). So the y - intercept \(b=2\). The slope - intercept form of a line is \(y=mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. Given \(m = 4\) and \(b = 2\), the equation of the line is \(y=4x + 2\).

Step2: Plot the y - intercept

First, plot the point \((0, 2)\) on the graph (this is the point where the line crosses the y - axis).

Step3: Use the slope to find another point

The slope \(m = 4=\frac{\text{rise}}{\text{run}}=\frac{4}{1}\). From the point \((0, 2)\), we can move up 4 units (rise) and 1 unit to the right (run). So starting from \((0, 2)\), moving up 4 units (from \(y = 2\) to \(y=2 + 4=6\)) and right 1 unit (from \(x = 0\) to \(x = 0+1 = 1\)) gives us the point \((1, 6)\). We can also move down 4 units and left 1 unit from \((0, 2)\) to get another point \((- 1,-2)\), but since our graph has non - negative \(x\) values up to 10 and non - negative \(y\) values up to 10, \((1, 6)\) is a good point to plot.

Step4: Draw the line

Draw a straight line through the points \((0, 2)\) and \((1, 6)\) (and other points found using the slope if needed) to represent the line \(y = 4x+2\).

Answer:

To graph the line:

1. Plot the point \((0, 2)\) (the y - intercept).
2. From \((0, 2)\), move up 4 units and right 1 unit to plot the point \((1, 6)\).
3. Draw a straight line through these two (and other) points. The line should pass through \((0, 2)\), \((1, 6)\), \((2, 10)\) (by continuing the slope: from \((1, 6)\), up 4, right 1 gives \((2, 10)\)) etc.