Questions: Find the slope and y-intercept of the line with equation x+6y=-6. Then graph the line. The slope is (Type an integer or a simplified fraction.)

$Find the slope and y-intercept of the line with equation x+6y=-6. Then graph the line. The slope is (Type an integer or a simplified fraction.)$

Transcript text: Find the slope and $y$-intercept of the line with equation $x+6 y=-6$. Then graph the line. The slope is $\square$ (Type an integer or a simplified fraction.)

Solution

Solution Steps

Step 1: Rewrite the equation in slope-intercept form

The given equation is $ x + 6y = -6 $. To find the slope and $ y $-intercept, we need to rewrite this equation in the slope-intercept form $ y = mx + b $.

Step 2: Solve for $ y $

\[ x + 6y = -6 \] \[ 6y = -x - 6 \] \[ y = -\frac{1}{6}x - 1 \]

Step 3: Identify the slope and $ y $-intercept

From the equation $ y = -\frac{1}{6}x - 1 $, we can see that the slope $ m $ is $ -\frac{1}{6} $ and the $ y $-intercept $ b $ is $ -1 $.

Final Answer

The slope is $ -\frac{1}{6} $.

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