The equation of a line is given by 6x + 2y = -4. Find the slope and the y-intercept. Then use them to graph the line.
Understand the Problem
The question provides a linear equation in standard form (6x + 2y = -4) and asks to find the slope and y-intercept of the line. Then, to use these two values to graph the line. To find the slope and y-intercept, you'll need to convert the equation to slope-intercept form (y = mx + b), where 'm' is the slope and 'b' is the y-intercept.
Answer
Slope: $-3$ Y-intercept: $-2$
Answer for screen readers
Slope: $-3$ Y-intercept: $-2$
Steps to Solve
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Isolate the 'y' term Start with the given equation $6x + 2y = -4$. Subtract $6x$ from both sides to isolate the term with 'y': $2y = -6x - 4$
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Solve for 'y' Divide both sides of the equation by 2 to solve for $y$: $y = \frac{-6x - 4}{2}$ $y = -3x - 2$
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Identify the slope The equation is now in slope-intercept form, $y = mx + b$, where 'm' is the slope. In this case, $m = -3$.
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Identify the y-intercept In the slope-intercept form, $y = mx + b$, 'b' represents the y-intercept. In this case, $b = -2$.
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Graph the line Plot the y-intercept at $(0, -2)$. Use the slope $-3$ (or $-3/1$) to find another point. Go down 3 units and right 1 unit from the y-intercept to find the point $(1, -5)$. Draw a line through these two points.
Slope: $-3$ Y-intercept: $-2$
More Information
The slope of $-3$ indicates that for every 1 unit increase in $x$, $y$ decreases by 3 units. The y-intercept of $-2$ indicates that the line crosses the y-axis at the point $(0, -2)$.
Tips
A common mistake is not dividing both terms on the right side of the equation by 2 when solving for y. For example, solving for y as $y = -3x - 4$ instead of $y = -3x -2$
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