Question

graph the line.
y = -2x - 5

Explanation:

Step1: Identify the slope and y-intercept

The equation is in slope - intercept form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. For \(y=-2x - 5\), the slope \(m=-2\) and the y - intercept \(b = - 5\). So, the line crosses the y - axis at the point \((0,-5)\).

Step2: Use the slope to find another point

The slope \(m=-2=\frac{-2}{1}\), which means from the y - intercept \((0,-5)\), we can move 1 unit to the right (increase \(x\) by 1) and 2 units down (decrease \(y\) by 2). So, from \((0,-5)\), moving 1 unit right and 2 units down gives us the point \((0 + 1,-5-2)=(1,-7)\). We can also move 1 unit to the left (decrease \(x\) by 1) and 2 units up (increase \(y\) by 2) from \((0,-5)\) to get \((-1,-3)\).

Step3: Plot the points and draw the line

Plot the points \((0,-5)\), \((1,-7)\) (or \((-1,-3)\)) on the coordinate plane. Then, use a straightedge to draw a line through these points. The line should extend infinitely in both directions.

(Note: Since this is a graphing problem, the final answer is the graph of the line \(y = - 2x-5\) passing through points like \((0,-5)\), \((1,-7)\), \((-1,-3)\) etc. )

Answer:

The line \(y=-2x - 5\) is graphed by plotting the y - intercept \((0,-5)\) and using the slope \(-2\) to find additional points (e.g., \((1,-7)\), \((-1,-3)\)) and then drawing a straight line through them.