The graph shows the words per minute Minka can type (1, 60) (7, 140)

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

GPT-4o mini · Answer

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.

Calculate the slope $m$ : $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}} = \frac{140 - 60}{7 - 1} = \frac{80}{6} = \frac{40}{3}$
Choose a point to use in the point-slope form. We can use the point (1, 60): $y - y_{1} = m (x - x_{1}) \Rightarrow y - 60 = \frac{40}{3} (x - 1)$
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.