Find the slope-intercept form of the equation of the line that passes through the given point an

step 1 In this problem, we are going to sketch a line that passes through the point 010 and has a slope

Find the slope-intercept form of the equation of the line...

Key Concepts

Slope-Intercept Form

The slope-intercept form of a linear equation is given by y = mx + b, where m represents the slope of the line and b represents the y-intercept. This form is widely used because it clearly shows both the steepness of the line and the point at which the line crosses the y-axis, allowing for straightforward graphing and interpretation of the line’s behavior.

Slope

The slope of a line, often denoted by m, measures the rate at which the line rises or falls. It is calculated as the change in y divided by the change in x (rise over run), and it indicates the direction and steepness of the line. A positive slope means the line is increasing, while a negative slope means the line is decreasing.

Y-Intercept

The y-intercept is the point at which a line crosses the y-axis, which occurs when x is zero. In the slope-intercept form of the line, y = mx + b, the y-intercept is provided directly by the constant term b, making it a crucial component for both the algebraic representation and graphing of the line.

Graphing Linear Equations

Graphing linear equations involves plotting key points such as the y-intercept and using the slope to determine additional points along the line. Once these points are identified, a straight line is drawn through them, providing a visual representation of the relationship expressed by the equation. This process is fundamental in coordinate geometry for understanding and analyzing linear relationships.

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