Use the graph to answer the question.

Question

The graph shows the words per minute Minka can type.
the points on the graph are (1, 60) ( 7, 140)
A coordinate plane going from 0 to 9 on the x-axis, which is labeled Time, minutes, in increments of 1 labeled every 1 unit and from 0 to 200 on the y-axis, which is labeled Words Typed, in increments of 20 labeled every 20 units.

Which is the equation of the line represented in the graph?

(1 point)
Responses

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

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

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

y=1403x+403
y is equal to 140 thirds x plus 40 thirds
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Answer 1

To find the equation of the line represented by the points \((1, 60)\) and \((7, 140)\), we first need to determine the slope (m) of the line. The formula for the slope between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:

\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

Using the given points:

• \((x_1, y_1) = (1, 60)\)
• \((x_2, y_2) = (7, 140)\)

Now we can calculate the slope:

\[ m = \frac{140 - 60}{7 - 1} = \frac{80}{6} = \frac{40}{3} \]

Now that we have the slope, we can use the point-slope form of the equation of a line, which is:

\[ y - y_1 = m(x - x_1) \]

Using the point \((1, 60)\):

\[ y - 60 = \frac{40}{3}(x - 1) \]

Now we'll distribute the slope:

\[ y - 60 = \frac{40}{3}x - \frac{40}{3} \]

Adding 60 to both sides to solve for \(y\):

\[ y = \frac{40}{3}x - \frac{40}{3} + 60 \]

Now convert 60 to a fraction with a denominator of 3:

\[ 60 = \frac{180}{3} \]

So, combining the terms yields:

\[ y = \frac{40}{3}x + \left(\frac{180}{3} - \frac{40}{3}\right) \] \[ y = \frac{40}{3}x + \frac{140}{3} \]

Thus, the equation of the line is:

\[ y = \frac{40}{3}x + \frac{140}{3} \]

From the options given, the correct response is:

y is equal to 40 thirds x plus 140 thirds.