What is 4x + y = 2?
Understand the Problem
The question is asking for the interpretation or solution of the equation 4x + y = 2, which often involves finding the values of x and y that satisfy this equation. The high-level approach will include rearranging the equation or substituting values to understand its graphical representation or solutions.
Answer
The equation $4x + y = 2$ rearranges to $y = 2 - 4x$ with a slope of $-4$ and a y-intercept of $2$.
Answer for screen readers
The equation $4x + y = 2$ can be rearranged to $y = 2 - 4x$, which has a slope of $-4$ and a y-intercept of $2$.
Steps to Solve
- Rearranging the Equation
To solve for one variable in terms of the other, we can rearrange the equation. Let's isolate $y$.
Starting with the equation:
$$ 4x + y = 2 $$
Subtract $4x$ from both sides:
$$ y = 2 - 4x $$
- Identifying the Slope and Intercept
Now that we have $y$ in terms of $x$, we can identify the slope and y-intercept of the equation $y = 2 - 4x$.
The equation can be written in the slope-intercept form $y = mx + b$, where:
- $m$ is the slope
- $b$ is the y-intercept
Here, $m = -4$ and $b = 2$.
- Graphing the Equation
When graphing the equation $y = 2 - 4x$, start at the y-intercept $(0, 2)$. Then, use the slope $-4$, which means for every 1 unit you move right along the x-axis, you move down 4 units on the y-axis.
- Finding Specific Values
You can choose specific values for $x$ to find corresponding values for $y$. For example, if $x = 0$:
$$ y = 2 - 4(0) = 2 $$
And if $x = 1$:
$$ y = 2 - 4(1) = -2 $$
So the points $(0, 2)$ and $(1, -2)$ are on the graph.
The equation $4x + y = 2$ can be rearranged to $y = 2 - 4x$, which has a slope of $-4$ and a y-intercept of $2$.
More Information
This equation represents a straight line in the Cartesian plane. The slope indicates that the line decreases steeply as x increases, while the intercept shows where the line crosses the y-axis.
Tips
- Forgetting to correctly rearrange the equation, which can lead to incorrect slopes or intercepts.
- Misinterpreting the slope: remember that a negative slope means the line goes down as you move to the right.
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