Question

graph this line using the slope and y - intercept:
( y = - \frac { 1 } { 9 } x - 1 )
click to select points on the graph.

Explanation:

Step1: Identify \( y \)-intercept

The equation is in \( y=mx + b \) form (\( m = -\frac{1}{9} \), \( b=-1 \)). The \( y \)-intercept is \( (0,b)=(0,-1) \).

Step2: Use slope to find another point

Slope \( m = \frac{\text{rise}}{\text{run}}=-\frac{1}{9} \). From \( (0,-1) \), run \( 9 \) (right) and rise \( - 1 \) (down). So new point is \( (0 + 9,-1-1)=(9,-2) \).

Step3: Draw the line

Connect \( (0,-1) \) and \( (9,-2) \) with a straight line. This line represents \( y = -\frac{1}{9}x - 1 \).

Answer:

To graph the line \( y = -\frac{1}{9}x - 1 \), first plot the \( y \)-intercept at \( (0,-1) \). Then, use the slope \( -\frac{1}{9} \) (which means for every 9 units we move to the right along the \( x \)-axis, we move 1 unit down along the \( y \)-axis) to find another point. For example, from \( (0,-1) \), moving 9 units right (to \( x = 9 \)) and 1 unit down gives the point \( (9,-2) \). Connect these two points to draw the line.