Question

Terri wrote the equation using slope-intercept form for the line that passes through the points (4, 6) and (–2, 3). Step 1: m = StartFraction 4 minus (negative 2) Over 6 minus 3 EndFraction = StartFraction 6 Over 3 EndFraction = 2 Step 2: 3 = 2 (negative 2) + b Step 3: 3 = negative 4 + b. 7 = b. Step 4: y = 2 x + 7 Which best describes Terri’s first error? In step 1, the slope of the line should be One-half. In step 2, she should have substituted the point (4, 6). In step 3, she should have subtracted 4 from both sides of the equation. In step 4, the m and b values should be switched.

Answer 1

y = (1/2)x + 4

Explanation:

As we move from the point (-2, 3) to the point (4, 6), x (the 'run') increases by 6 and y (the 'rise')increases by 3. Therefore the slope of the line connecting the two points is m = rise / run = 3/6, or m = 1/2.

We want the slope-intercept form of the equation of this line. The basic form is y = mx + b. Arbitrarily choosing to use the point (4, 6) and using m = 1/2, we get:

6 = (1/2)(4) + b, or b = 4.

Then the desired equation is y = mx + b, or y = (1/2)x + 4

Answer 2

(A) In step 1, the slope of the line should be One-half

Explanation:

Terri calculated the slope as (x1 -x2)/(y1 -y2). Her first error was using this formula, when she should have used ...

m = (y1 -y2)/(x1 -x2)

= (6 -3)/(4 -(-2)) = 3/6 = 1/2

The best of the offered descriptions is ...

In step 1, the slope of the line should be One-half