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 $2$.

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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