Converting Linear Equations: 10x + 2y = -10 in Slope-Intercept Form
In algebra, linear equations can be expressed in various forms, including the slope-intercept form. The slope-intercept form is a popular way to express linear equations, as it provides valuable information about the graph of the equation. In this article, we will explore how to convert the linear equation 10x + 2y = -10 into slope-intercept form.
What is Slope-Intercept Form?
The slope-intercept form of a linear equation is written in the form:
y = mx + b
where:
- m is the slope (a measure of how steep the line is)
- b is the y-intercept (the point where the line crosses the y-axis)
Converting 10x + 2y = -10 to Slope-Intercept Form
To convert the given equation 10x + 2y = -10 to slope-intercept form, we need to isolate the y variable. We can do this by subtracting 10x from both sides of the equation, resulting in:
2y = -10 - 10x
Next, we can divide both sides of the equation by 2 to solve for y:
y = (-10 - 10x) / 2
Simplifying the equation, we get:
y = -5 - 5x
Slope-Intercept Form: y = -5 - 5x
The equation y = -5 - 5x is in slope-intercept form, where:
- The slope (m) is -5, indicating a downward slope.
- The y-intercept (b) is -5, indicating that the line crosses the y-axis at the point (0, -5).
In conclusion, the linear equation 10x + 2y = -10 can be converted to slope-intercept form as y = -5 - 5x, providing valuable insights into the graph of the equation.
