Question

graph the following features: • y-intercept = -1 • slope = \\(\frac{2}{5}\\)

Explanation:

Step1: Plot the y - intercept

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

Step2: Use the slope to find another point

The slope \(m = \frac{2}{5}\), which means for a run of \(5\) units (change in \(x\)) to the right, we have a rise of \(2\) units (change in \(y\)). Starting from the point \((0,-1)\), if we move \(5\) units to the right (increase \(x\) by \(5\)) and \(2\) units up (increase \(y\) by \(2\)), we get the point \((0 + 5,-1+2)=(5,1)\). We can also move \(5\) units to the left (decrease \(x\) by \(5\)) and \(2\) units down (decrease \(y\) by \(2\)) from \((0,-1)\) to get the point \((0 - 5,-1-2)=(-5,-3)\).

Step3: Draw the line

Draw a straight line passing through the points we found (e.g., \((0,-1)\) and \((5,1)\)) to represent the linear equation \(y=\frac{2}{5}x - 1\).

Answer:

The graph is a straight line passing through \((0, - 1)\) with a slope of \(\frac{2}{5}\) (passing through other points like \((5,1)\) or \((-5,-3)\) as calculated). The line is drawn by connecting these points on the given coordinate grid.