Question

Use the given points to choose the correct linear equation in slope-intercept form.
(2,-1) and (4,5)

A) y=1/3x-7
B) y=3x-2
C) y=3x-7
D) y=1/3x-2

Answer 1

To find the correct linear equation in slope-intercept form (y = mx + b) that passes through the points (2, -1) and (4, 5), we need to calculate the slope (m) and then the y-intercept (b).

1. **Calculate the slope (m)** using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Plugging in the points (2, -1) as \((x_1, y_1)\) and (4, 5) as \((x_2, y_2)\):
\[
m = \frac{5 - (-1)}{4 - 2} = \frac{5 + 1}{2} = \frac{6}{2} = 3
\]

2. **Use the slope to find the y-intercept (b)**. We can use one of the points and the slope to find the y-intercept. Using the point (2, -1):
\[
y = mx + b \rightarrow -1 = 3(2) + b
\]
\[
-1 = 6 + b \rightarrow b = -1 - 6 = -7
\]

3. **Write the equation in slope-intercept form**:
\[
y = 3x - 7
\]

Now, we can match the derived equation with the given options:

A) \( y = \frac{1}{3}x - 7 \)
B) \( y = 3x - 2 \)
C) \( y = 3x - 7 \)
D) \( y = \frac{1}{3}x - 2 \)

The correct answer is:

**C) y = 3x - 7**