Question

The graph shows the words per minute Minka can type (1, 60) (7, 140)
Which is the equation of the line represented in the graph? (1 point) Responses y=40/3x+140/3 y is equal to 40 thirds x plus 140 thirds y=3/140x−7/2 y is equal to 3 over 140 x minus 7 halves y=140/3x+40/3 y is equal to 140 thirds x plus 40 thirds y=40/3x+50

Answer 1

To find the equation of the line passing through the points (1, 60) and (7, 140), we can first determine the slope \( m \) and then use the point-slope form of the equation of a line.

1. **Calculate the slope \( m \)**:
\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{140 - 60}{7 - 1} = \frac{80}{6} = \frac{40}{3}
\]

2. **Choose a point to use in the point-slope form**. We can use the point (1, 60):
\[
y - y_1 = m(x - x_1) \quad \Rightarrow \quad y - 60 = \frac{40}{3}(x - 1)
\]

3. **Simplify the equation**:
\[
y - 60 = \frac{40}{3}x - \frac{40}{3}
\]
\[
y = \frac{40}{3}x - \frac{40}{3} + 60
\]
To combine, convert 60 into thirds:
\[
60 = \frac{180}{3}
\]
So,
\[
y = \frac{40}{3}x - \frac{40}{3} + \frac{180}{3}
\]
\[
y = \frac{40}{3}x + \frac{140}{3}
\]

Therefore, the equation of the line is:
\[
y = \frac{40}{3}x + \frac{140}{3}
\]

So the correct response is:
**y = 40/3x + 140/3**.