Question

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

Explanation:

Step1: Recall Slope-Intercept Form

The slope - intercept form of a linear equation is \(y = mx + b\), where \(m\) is the slope and \(b\) is the \(y\) - intercept. Given that \(m=-2\) and \(b = 1\), the equation of the line is \(y=-2x + 1\).

Step2: Plot the Y - intercept

The \(y\) - intercept is the point where the line crosses the \(y\) - axis. When \(x = 0\), \(y=b = 1\). So we plot the point \((0,1)\) on the coordinate plane.

Step3: Use the Slope to Find Another Point

The slope \(m=\frac{\text{rise}}{\text{run}}\). The slope \(m=-2=\frac{- 2}{1}\) (or \(\frac{2}{-1}\)). Starting from the point \((0,1)\), if we use the slope \(\frac{\text{rise}}{\text{run}}=\frac{-2}{1}\), we move down 2 units (because the rise is - 2) and then 1 unit to the right (because the run is 1). This gives us the point \((0 + 1,1-2)=(1,-1)\). We can also use the slope \(\frac{2}{-1}\): move up 2 units and 1 unit to the left from \((0,1)\) to get the point \((0 - 1,1 + 2)=(-1,3)\).

Step4: Draw the Line

After plotting two or more points (e.g., \((0,1)\) and \((1,-1)\) or \((0,1)\) and \((-1,3)\)), we draw a straight line passing through these points.

(Note: Since the problem is about graphing, the final answer is the graph of the line \(y = - 2x+1\) with \(y\) - intercept at \((0,1)\) and slope - 2. To describe the graphing process as above, and the visual graph should have a line starting at \((0,1)\), going down 2 units for every 1 unit to the right (or up 2 units for every 1 unit to the left).)

Answer:

The graph is a straight line with \(y\) - intercept at \((0,1)\) and slope \(-2\) (equation \(y=-2x + 1\)) plotted on the given coordinate plane.