Which equation represents the slope-intercept form of a line?

Which equation represents the slope-intercept form of a line?

• A. y = mx + b
• B. Ax + By = C
• C. a(b + c) = ab + ac
• D. y - y1 = m(x - x1)

Answer: (A)

Recognize slope-intercept form: an equation written with y isolated on one side, showing the slope m as the coefficient of x and the y-intercept b as the constant term. This directly takes the shape y = mx + b, where m tells how steep the line is and b tells where it crosses the y-axis. The form y = mx + b is the one that explicitly displays both the slope and the intercept, which is what slope-intercept form means. Other expressions describe lines in different ways: Ax + By = C is standard form and would need solving for y to become slope-intercept; a(b + c) = ab + ac is just a distributive property, not a line equation; y - y1 = m(x - x1) is point-slope form, which can be rearranged to slope-intercept form by solving for y, yielding y = mx + (y1 - m x1).

Recognize slope-intercept form: an equation written with y isolated on one side, showing the slope m as the coefficient of x and the y-intercept b as the constant term. This directly takes the shape y = mx + b, where m tells how steep the line is and b tells where it crosses the y-axis.

The form y = mx + b is the one that explicitly displays both the slope and the intercept, which is what slope-intercept form means. Other expressions describe lines in different ways: Ax + By = C is standard form and would need solving for y to become slope-intercept; a(b + c) = ab + ac is just a distributive property, not a line equation; y - y1 = m(x - x1) is point-slope form, which can be rearranged to slope-intercept form by solving for y, yielding y = mx + (y1 - m x1).