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=1403x+403
𝑦
=
140
3
𝑥
+
40
3
y is equal to 140 thirds x plus 40 thirds

y=3140x−72
𝑦
=
3
140
𝑥
−
7
2
y is equal to 3 over 140 x minus 7 halves

y=403x+50
𝑦
=
40
3
𝑥
+
50
y is equal to 40 thirds x plus 50

y=403x+1403

Answer 1

To determine the equation of the line represented by the points (1, 60) and (7, 140), we need to find the slope (m) and the y-intercept (b) of the line using the slope-intercept form \( y = mx + b \).

1. **Calculate the slope (m)**:

The formula for the slope between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Plugging in the points \((1, 60)\) and \((7, 140)\):
\[
m = \frac{140 - 60}{7 - 1} = \frac{80}{6} = \frac{40}{3}
\]

2. **Use the slope to find the y-intercept (b)**:

We can use the slope-intercept form \( y = mx + b \) and take one of the points to find b. Using the point (1, 60):
\[
60 = \frac{40}{3}(1) + b
\]

Solving for b:
\[
60 = \frac{40}{3} + b
\]
\[
b = 60 - \frac{40}{3}
\]
To subtract, convert 60 into thirds:
\[
60 = \frac{180}{3}
\]
So,
\[
b = \frac{180}{3} - \frac{40}{3} = \frac{140}{3}
\]

3. **Write the equation of the line**:

Now that we have both m and b, the equation is:
\[
y = \frac{40}{3}x + \frac{140}{3}
\]

This matches with the response \( y = \frac{40}{3}x + \frac{140}{3} \).

Thus, the correct answer is:
**y = \(\frac{40}{3}\)x + \(\frac{140}{3}\)**.