FTCE Professional Education Practice Exam

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What does the equation y - ya = m(X - xa) represent?

The slope of a line
The y-intercept of a line
The point-slope form of a line
The distance formula

The correct answer is: The point-slope form of a line

The equation y - ya = m(X - xa) is known as the point-slope form of a linear equation. This form is particularly useful in mathematics because it allows you to easily write the equation of a line when you know the slope (m) and a specific point on the line (xa, ya). In this equation, "m" represents the slope, while (xa, ya) is a point through which the line passes. Rearranging the equation can lead to the slope-intercept form (y = mx + b), but the given form directly emphasizes the relationship between the slope and the coordinates of the line. Understanding this form is crucial for graphing linear equations, solving problems involving lines, and analyzing how changes in slope or points affect the graph of the equation, making it a fundamental concept in algebra and coordinate geometry.