Question

graph this line using the slope and y - intercept:

$y = - \frac { 1 } { 6 } x + 8$

click to select points on the graph.

Explanation:

Step1: Identify the \( y \)-intercept

The equation is in slope - intercept form \( y=mx + b \), where \( b \) is the \( y \)-intercept. Here, \( b = 8 \), so the line crosses the \( y \)-axis at \( (0,8) \).

Step2: Use the slope to find another point

The slope \( m=-\frac{1}{6} \). Starting from \( (0,8) \), if \( x \) increases by \( 6\) (denominator of the slope), \( y \) decreases by \( 1\) (numerator of the slope). So, \( y=-\frac{1}{6}(6)+8=-1 + 8=7 \), giving the point \( (6,7) \).

Step3: Draw the line

Plot the points \( (0,8) \) and \( (6,7) \) on the coordinate plane and draw a straight line through them. This line represents the equation \( y = -\frac{1}{6}x+8 \).

Answer:

To graph \( y = -\frac{1}{6}x + 8 \), first plot the \( y \)-intercept at \( (0,8) \). Then, use the slope \( -\frac{1}{6} \) (which means for every 6 units you move to the right along the \( x \)-axis, you move 1 unit down along the \( y \)-axis) to find another point. For example, from \( (0,8) \), moving 6 units right (to \( x = 6 \)) and 1 unit down gives the point \( (6,7) \). Connect these points to draw the line.