Question

Jolon used the slope-intercept form to write the equation of a line with slope 3 that passes through the point (5, –2). His work is shown below.

Step 1: Negative 2 = 3 (5) + b
Step 2: negative 2 = 15 + b
Step 3: Negative 2 + 15 = 15 + 15 + b
Step 4: Negative 13 = b
Step 5: y = 3x – 13

Answer 1

Jolon mistakingly added 15 to both sides of the equation in Step 3. Step 3's correct answer is -2 + 15 = -15 + 15 + b, Step 4's correct answer is -17 = b, and Step 5's correct answer is y = 3x - 17

Explanation:

It appears that you're trying to identify Jolon's mistake. If you're trying to do something else, type it in the comments as the answer I'm providing identifies Jolon's mistake.

• In Step 3, Jolon added 15 to both sides.
• However, doing this would have given you (-2 + 15) = (15 + 15 + b), which becomes -13 = 30 + b.
• In order to eliminate 15 on the right-hand side of the equaiton, Jolon instead needed to subtract 15 from both sides, which gives you (-2 - 15) = (15 - 15 + b).
• This simplifies to -17 = b.

• You can check that -17 = b is correct by plugging in 3 for m, (5, -2) for (x, y), and -17 for b in the slope-intercept form (y = mx + b) and checking that you get the same answer on both sides of the equation:

-2 = 3(5) - 17

-2 = 15 - 17

-2 = -2

Thus, Step 3 should be: (-2 + 15) = (-15 + 15 + b), Step 4 should be: -17 = b, and Step 5 should be: y = 3x - 17

Answer 2

The answer is:

y = 3x - 17

Work/explanation:

We need to write the equation in slope intercept form.

y = mx + b

where m = slope and b = y intercept; x and y are the co-ordinates of a point on the line

Plug in the data

`\sf{y=mx+b}`

`\sf{y=3x+b}`

`\sf{-2=3(5)+b}`

`\sf{-2=15+b}`

`\sf{-2-15=b}`

`\sf{-17=b}`

Hence, the answer is y = 3x - 17; Jolon was wrong because he shouldn't have added 15 to each side; he should have subtracted it instead. Also, 15 + 15 doesn't cancel out to 0. As a result, he got a wrong answer. The right one is y = 3x - 17.