y=mx+b example; y=mx+b calculator; writing linear equations in slope-intercept form answer key; write equation in slope intercept form calculator; standard form equation; slope-intercept form examples; point slope form calculator; how to find the y-intercept
The Correct Answer and Explanation is :
The correct answer is: the slope ( m = -2 ) and the y-intercept ( b = 3 )
Certainly! Let’s explore the slope-intercept form of linear equations, which is given by the formula:
[
y = mx + b
]
where:
- ( y ) is the dependent variable.
- ( m ) is the slope of the line.
- ( x ) is the independent variable.
- ( b ) is the y-intercept (the value of ( y ) when ( x = 0 )).
Example of a Linear Equation in Slope-Intercept Form
Consider the equation:
[
y = 2x + 3
]
In this case:
- The slope ( m = 2 ), which means for every unit increase in ( x ), ( y ) increases by 2 units.
- The y-intercept ( b = 3 ), indicating that the line crosses the y-axis at the point (0, 3).
Finding the Slope and Y-Intercept
To convert a linear equation into slope-intercept form, rearranging may be necessary. For example, consider the equation:
[
4x + 2y = 6
]
To convert it to slope-intercept form, solve for ( y ):
- Subtract ( 4x ) from both sides:
[
2y = -4x + 6
] - Divide every term by 2:
[
y = -2x + 3
]
Here, the slope ( m = -2 ) and the y-intercept ( b = 3 ).
Calculators and Resources
- Slope-Intercept Form Calculator: Online calculators can assist in converting equations to slope-intercept form by inputting standard form equations.
- Point-Slope Form: An alternate form is ( y – y_1 = m(x – x_1) ), useful when a point ((x_1, y_1)) on the line is known along with the slope ( m ).
Conclusion
Understanding the slope-intercept form is essential in algebra and helps in graphing linear equations, predicting outcomes, and understanding relationships between variables. Identifying the slope and y-intercept is crucial for interpreting and analyzing linear relationships in various applications.