The equation 3x + 2y = 12 is given. What is the slope of this line?
A3
B-3/2
C2
D6
To read slope and y-intercept, the equation must be solved for y first. Subtract 3x from both sides: 2y = -3x + 12. Divide by 2: y = -(3/2)x + 6. Now the slope is the coefficient of x, which is -3/2. The common mistake is reading the coefficient of x from the unsolved equation (3) or forgetting to divide the coefficient by 2 along with the constant.
Question 2 Multiple Choice
A streaming service costs $8 per month plus a one-time $15 setup fee. The equation y = 8x + 15 models total cost y after x months. What does the value 15 represent?
AThe cost increases by $15 each month
BThe total cost after 15 months
CThe cost before any months have passed — what you owe at month zero
DThe number of months until the service breaks even
In y = mx + b, b is the y-intercept — the value of y when x = 0. Here, x = 0 means zero months have passed, so y = 8(0) + 15 = 15. This is the setup fee paid before any monthly charges accrue. The value 8 (the coefficient m) is the rate — cost increases by $8 per month. Confusing m and b is the most common error with slope-intercept interpretation.
Question 3 True / False
In y = mx + b, b alone is the y-coordinate of the point where the line crosses the y-axis, and the full y-intercept point is (0, b).
TTrue
FFalse
Answer: True
When x = 0, the equation becomes y = m(0) + b = b. So the line crosses the y-axis at the point (0, b); b is the y-coordinate of that point. This distinction matters when graphing: the starting point to plot is (0, b), not just a height of b floating without location.
Question 4 True / False
For the equation 4x + 2y = 10, the slope is 4 and the y-intercept is 10.
TTrue
FFalse
Answer: False
You cannot read slope and y-intercept from an equation not solved for y. First isolate y: subtract 4x to get 2y = -4x + 10, then divide by 2 to get y = -2x + 5. The slope is -2 (not 4) and the y-intercept is 5 (not 10). Skipping the division step produces the coefficient of x in the original equation — a systematic error that multiplies both m and b by the missing factor.
Question 5 Short Answer
Why must you solve an equation for y before reading off the slope and y-intercept? What specific error occurs if you skip this step with an equation like 6x + 3y = 18?
Think about your answer, then reveal below.
Model answer: Slope-intercept form requires y to be isolated: y = mx + b. Only then does the coefficient of x equal m and the constant equal b. For 6x + 3y = 18, solving gives y = -2x + 6 (slope -2, y-intercept 6). Without solving, a student might read slope as 6 and y-intercept as 18 — both wrong by a factor of 3, because the division by the coefficient of y was never applied.
The key is that slope-intercept form demands a coefficient of exactly 1 in front of y. When y has a different coefficient, every other term must be divided by it too. Missing this produces a slope and y-intercept that are both scaled incorrectly, a systematic error that can go unnoticed without checking by substituting a point.