Question

Which is the equation of the line represented in the graph (7, 140) and (1, 60)?

(1 point)
Responses

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

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

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

y=3/140x−7/2

Answer 1

To find the equation of the line given the points (7, 140) and (1, 60), we start by calculating the slope (m) of the line using the formula:

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

Let (x₁, y₁) = (7, 140) and (x₂, y₂) = (1, 60). Plugging in the values:

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

Now that we have the slope \( m = \frac{40}{3} \), we can use the point-slope form of the equation of the line, which is:

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

Using point (7, 140):

\[
y - 140 = \frac{40}{3}(x - 7)
\]

Distributing \( \frac{40}{3} \):

\[
y - 140 = \frac{40}{3}x - \frac{40}{3} \cdot 7
\]
\[
y - 140 = \frac{40}{3}x - \frac{280}{3}
\]

Adding 140 to both sides to isolate \( y \):

\[
y = \frac{40}{3}x + 140 - \frac{280}{3}
\]

Converting 140 to thirds:

\[
140 = \frac{420}{3}
\]

Now substituting this into the equation:

\[
y = \frac{40}{3}x + \frac{420}{3} - \frac{280}{3}
\]
\[
y = \frac{40}{3}x + \frac{140}{3}
\]

The equation of the line is:

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

This is consistent with the response "𝑦 = 40/3 𝑥 + 140/3".

Thus, the correct answer is:

**y = 40/3x + 140/3**.