Graph a linear equation with a slope of -1/5 and a positive y-intercept.

Steps to Solve

1. Identify the slope and y-intercept

The slope of the linear equation is given as $-\frac{1}{5}$. This means for every 5 units you move to the right on the x-axis, you move down 1 unit on the y-axis. Since it is specified that there's a positive y-intercept, we will denote the y-intercept as $b$ (a positive value).

2. Write the equation in slope-intercept form

The slope-intercept form of a linear equation is given by:

$$ y = mx + b $$

Where $m$ is the slope, and $b$ is the y-intercept. Substituting the known values:

$$ y = -\frac{1}{5}x + b $$

3. Plot the y-intercept

Choose a positive value for the y-intercept, for example $b = 2$. Thus, the equation becomes:

$$ y = -\frac{1}{5}x + 2 $$

Now, plot the point (0, 2) on the graph.

4. Use the slope to find another point

Starting from the y-intercept (0, 2), use the slope $-\frac{1}{5}$. This means from the point (0, 2), move 5 units to the right (to x = 5) and 1 unit down (to y = 1), giving the point (5, 1). Plot this point.

5. Draw the line

Connect the two points (0, 2) and (5, 1) with a straight line. Extend the line across the graph, ensuring it maintains the linear relationship defined by the slope.