Question

graph the following features: - y-intercept = -6 - slope = -1/2

Explanation:

Step1: Plot the y - intercept

The y - intercept is the point where the line crosses the y - axis. Given that the y - intercept is \(-6\), we plot the point \((0, - 6)\) on the coordinate plane.

Step2: Use the slope to find another point

The slope \(m=-\frac{1}{2}\) can be interpreted as \(\frac{\text{rise}}{\text{run}}\). A slope of \(-\frac{1}{2}\) means that for every \(2\) units we move to the right (run = \(2\)) along the x - axis, we move down \(1\) unit (rise=\(- 1\)) along the y - axis. Starting from the point \((0,-6)\), if we move \(2\) units to the right (x increases by \(2\), so \(x = 0+2 = 2\)) and \(1\) unit down (y decreases by \(1\), so \(y=-6 - 1=-7\)), we get the point \((2,-7)\). We can also move in the opposite direction: for every \(2\) units we move to the left (run=\(-2\)), we move up \(1\) unit (rise = \(1\)). Starting from \((0,-6)\), moving \(2\) units left (\(x = 0-2=-2\)) and \(1\) unit up (\(y=-6 + 1=-5\)) gives the point \((-2,-5)\).

Step3: Draw the line

Draw a straight line passing through the points we have plotted (such as \((0,-6)\), \((2,-7)\), \((-2,-5)\) etc.).

(Note: Since the question is about graphing, the final answer is the graph with the line passing through the points determined by the y - intercept and the slope. If we were to write the equation of the line, it would be \(y=-\frac{1}{2}x - 6\), but the main task here is graphing. To describe the graph: It is a straight line with a negative slope (\(-\frac{1}{2}\)) crossing the y - axis at \((0,-6)\) and passing through other points as calculated from the slope.)

Answer:

The graph is a straight line with y - intercept at \((0, - 6)\) and slope \(-\frac{1}{2}\), passing through points like \((2,-7)\) and \((-2,-5)\) (or other points determined by the slope from the y - intercept). The equation of the line is \(y =-\frac{1}{2}x-6\) and it is graphed by plotting \((0, - 6)\) and using the slope to find additional points and then drawing the line through them.