What is the equation of a line in slope-intercept form?

What is the equation of a line in slope-intercept form?

• A. y = mx + b
• B. y = x + b
• C. m = (y2 - y1)/(x2 - x1)
• D. y - y1 = m(x - x1)

Answer: (A)

The slope-intercept form of the equation of a line is expressed as y = mx + b. In this formula, 'm' represents the slope of the line, which indicates the steepness and direction of the line, while 'b' represents the y-intercept, which is the point at which the line crosses the y-axis. This formula is particularly useful because it allows one to quickly identify the slope and y-intercept of a line, making graphing easy. The other options provided represent different concepts related to lines. The second option, y = x + b, does not include the slope variable m and therefore is not in the standard slope-intercept form. The third option, m = (y2 - y1)/(x2 - x1), is the formula for calculating the slope between two points (x1, y1) and (x2, y2), but it does not define the line's equation itself. The fourth option, y - y1 = m(x - x1), is the point-slope form of a line, which is useful for deriving the line's equation if you know a specific point on the line and the slope, but it also deviates from the desired slope-intercept form.

The slope-intercept form of the equation of a line is expressed as y = mx + b. In this formula, 'm' represents the slope of the line, which indicates the steepness and direction of the line, while 'b' represents the y-intercept, which is the point at which the line crosses the y-axis. This formula is particularly useful because it allows one to quickly identify the slope and y-intercept of a line, making graphing easy.

The other options provided represent different concepts related to lines. The second option, y = x + b, does not include the slope variable m and therefore is not in the standard slope-intercept form. The third option, m = (y2 - y1)/(x2 - x1), is the formula for calculating the slope between two points (x1, y1) and (x2, y2), but it does not define the line's equation itself. The fourth option, y - y1 = m(x - x1), is the point-slope form of a line, which is useful for deriving the line's equation if you know a specific point on the line and the slope, but it also deviates from the desired slope-intercept form.