5x minus 2y equals minus 10

Understand the Problem

The question is presenting a linear equation in two variables (x and y) and appears to seek a solution or simplification for the equation.

Answer

The simplified equation is $y = \frac{5}{2}x + 5$.

Steps to Solve

Identify the equation The given equation is $5x - 2y = -10$.
Rearrange for y To find the value of $y$, rearrange the equation. First, we will isolate $2y$:

$$ 2y = 5x + 10 $$

Next, divide both sides by 2 to solve for $y$:

$$ y = \frac{5x + 10}{2} $$

Simplify the expression Let's distribute the division across the terms in the numerator:

$$ y = \frac{5x}{2} + \frac{10}{2} $$

This simplifies to:

$$ y = \frac{5}{2}x + 5 $$

Now we have the equation in slope-intercept form.

Understanding the slope-intercept form In the slope-intercept form $y = mx + b$, $m$ represents the slope and $b$ represents the y-intercept. Here, the slope is $\frac{5}{2}$ and the y-intercept is $5$.

The simplified equation in slope-intercept form is:

$$ y = \frac{5}{2}x + 5 $$

More Information

The equation $y = \frac{5}{2}x + 5$ indicates a line with a slope of $\frac{5}{2}$, meaning for every 2 units we move to the right on the x-axis, we move up 5 units on the y-axis. The line crosses the y-axis at the point (0, 5).

Tips

Forgetting to distribute correctly when simplifying can lead to errors. Always double-check your arithmetic when rearranging equations.

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