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 move up 4 units (since rise is 4) and to the right 1 unit (since run is 1). So, starting at \((0, 2)\), adding 1 to the \(x\) - coordinate and 4 to the \(y\) - coordinate, we get the point \((0 + 1,2+4)=(1, 6)\). We can also move down 4 units and left 1 unit from \((0, 2)\) to get another point \((0-1,2 - 4)=(- 1,-2)\), but since our graph has non - negative \(x\) - 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 extend it in both directions).

Answer:

The line is graphed by plotting the point \((0, 2)\) (y - intercept) and using the slope \(4\) to find another point (e.g., \((1, 6)\)) and then drawing a straight line through these points. The equation of the line is \(y = 4x+2\).