Question

graph the line.
$y=-dfrac{2}{5}x - 2$

Explanation:

Step1: Identify the y-intercept

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

Step2: Use the slope to find another point

The slope \(m =-\frac{2}{5}\). The slope is \(\frac{\text{rise}}{\text{run}}\), which means for a run of 5 units (moving 5 units to the right along the x - axis), the rise is - 2 units (moving 2 units down along the y - axis). Starting from the y - intercept \((0,-2)\), if we move 5 units to the right (x increases by 5) and 2 units down (y decreases by 2), we get the point \((0 + 5,-2-2)=(5,-4)\). We can also use a run of - 5 (move 5 units to the left) and a rise of 2 (move 2 units up) from \((0,-2)\) to get the point \((0 - 5,-2 + 2)=(-5,0)\).

Step3: Draw the line

Plot the points \((0,-2)\), \((5,-4)\) (or \((-5,0)\)) on the coordinate plane and then draw a straight line passing through these points.

(Note: Since this is a graphing problem, the final answer is the graph of the line \(y =-\frac{2}{5}x-2\) passing through the points \((0, - 2)\) and other points found using the slope, like \((5,-4)\) or \((-5,0)\).)

Answer:

Step1: Identify the y-intercept

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

Step2: Use the slope to find another point

The slope \(m =-\frac{2}{5}\). The slope is \(\frac{\text{rise}}{\text{run}}\), which means for a run of 5 units (moving 5 units to the right along the x - axis), the rise is - 2 units (moving 2 units down along the y - axis). Starting from the y - intercept \((0,-2)\), if we move 5 units to the right (x increases by 5) and 2 units down (y decreases by 2), we get the point \((0 + 5,-2-2)=(5,-4)\). We can also use a run of - 5 (move 5 units to the left) and a rise of 2 (move 2 units up) from \((0,-2)\) to get the point \((0 - 5,-2 + 2)=(-5,0)\).

Step3: Draw the line

Plot the points \((0,-2)\), \((5,-4)\) (or \((-5,0)\)) on the coordinate plane and then draw a straight line passing through these points.

(Note: Since this is a graphing problem, the final answer is the graph of the line \(y =-\frac{2}{5}x-2\) passing through the points \((0, - 2)\) and other points found using the slope, like \((5,-4)\) or \((-5,0)\).)