Question

What is the equation of a line given a slope and a point?

A) y = mx + b
B) y - y_1 = m(x - x_1)
C) y = b + mx
D) y = x + m

Answer 1

The equation of a line with a given slope and a point is best represented using the point-slope form, y - y1 = m(x - x1). Alternatively, the slope-intercept form, y = mx + b, can be used when the slope and y-intercept are known.

Step-by-step explanation:

The equation of a line given a slope and a point is represented by the formula y - y1 = m(x - x1), where m is the slope and (x1, y1) is the point on the line. This formula is known as the point-slope form. The slope, m, is defined as the rise divided by the run, and it describes the steepness of the line. When you have the slope and the y-intercept, you can use the slope-intercept form, which is written as y = mx + b. Here, b represents the y-intercept, which is where the line crosses the y-axis. Both of these representations are crucial in depicting a linear equation graphically and algebraically.