A linear function passes through (0, 4) with slope -2. What is its equation?

A linear function passes through (0, 4) with slope -2. What is its equation?

• A. y = 2x + 4
• B. y = -2x + 4
• C. y = -2x - 4
• D. y = x - 4

Answer: (B)

In slope-intercept form, a line is y = mx + b, where m is the slope and b is the y-intercept. Since the line passes through (0, 4), the y-intercept is 4. The slope is given as -2. Put them together to get y = -2x + 4. This satisfies both the slope and the point: when x = 0, y = 4, and for each increase of x by 1, y decreases by 2. Other options would change either the slope or the intercept: a positive slope of 2 would contradict the given slope; an intercept of -4 would place the line crossing the y-axis at -4; a slope of 1 with an intercept of -4 also mismatches the provided values.

In slope-intercept form, a line is y = mx + b, where m is the slope and b is the y-intercept. Since the line passes through (0, 4), the y-intercept is 4. The slope is given as -2. Put them together to get y = -2x + 4. This satisfies both the slope and the point: when x = 0, y = 4, and for each increase of x by 1, y decreases by 2.

Other options would change either the slope or the intercept: a positive slope of 2 would contradict the given slope; an intercept of -4 would place the line crossing the y-axis at -4; a slope of 1 with an intercept of -4 also mismatches the provided values.