Question

graph this line using the slope and y-intercept:
$y = -\frac{1}{10}x + 8$
click to select points on the graph.

Explanation:

Step1: Identify y-intercept

The equation is in slope - intercept form \(y = mx + b\), where \(b\) is the y - intercept. For \(y=-\frac{1}{10}x + 8\), \(b = 8\). So the y - intercept is the point \((0,8)\). Plot this point on the graph (it lies on the y - axis at \(y = 8\)).

Step2: Use slope to find next point

The slope \(m=-\frac{1}{10}\). The slope is \(\frac{\text{rise}}{\text{run}}\), so \(\text{rise}=- 1\) and \(\text{run}=10\). From the point \((0,8)\), move down 1 unit (because rise is - 1) and then move 10 units to the right (because run is 10). This gives the point \((0 + 10,8-1)=(10,7)\). Alternatively, we can also use a positive run and negative rise or negative run and positive rise. For example, if we take \(\text{run}=- 10\) and \(\text{rise}=1\), from \((0,8)\), move left 10 units and up 1 unit to get the point \((0-10,8 + 1)=(-10,9)\).

Step3: Draw the line

After plotting at least two points (e.g., \((0,8)\) and \((10,7)\) or \((0,8)\) and \((-10,9)\)), draw a straight line passing through these points.

Answer:

To graph \(y =-\frac{1}{10}x + 8\):

1. Plot the y - intercept \((0,8)\) (on the y - axis at \(y = 8\)).
2. Use the slope \(m =-\frac{1}{10}\): from \((0,8)\), move down 1 unit and right 10 units to get \((10,7)\) (or left 10 units and up 1 unit to get \((-10,9)\)).
3. Draw a straight line through the plotted points.