To determine which graph matches the linear equation \( 6x + y = -4 \), we can first rewrite the equation in slope-intercept form (i.e., \( y = mx + b \)), where \( m \) is the slope and \( b \) is the y-intercept.
Starting with the equation:
\[ 6x + y = -4 \]
we can isolate \( y \) by subtracting \( 6x \) from both sides:
\[ y = -6x - 4 \]
From this equation, we see that the slope (\( m \)) is \(-6\) and the y-intercept (\( b \)) is \(-4\).
- The y-intercept means that the graph will cross the y-axis at the point (0, -4).
- The negative slope means that for every 1 unit increase in \( x \), \( y \) will decrease by 6 units, indicating a steep downward line.
To find the corresponding graph, look for these characteristics:
- The line should intersect the y-axis at (0, -4).
- The line should be steep and move downward from left to right.
If you have a set of graphs, look for one that matches these criteria. If you want further assistance, please describe the options available or provide a visual reference, and I can help you identify the correct graph.
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