Question

Write the equation of the line passing through the points (-7, 5) and (7, 1)

Answer 1

y = -2/7(x) + 3

Explanation:

The equation of a line can be stated as y = mx + b, where m is the slope and b is the y-intercept (the value of the function when x = 0). To find the equation of the line, we'll start by finding the slope.

The slope can be expressed as
`\frac{y_(2) - y_(1)}{x_(2)-{x_1}}`

Substituting in our coordinates, we have:

`m = (1 - 5)/(7 - (-7)) = (-4)/(7 + 7) = (-4)/(14)`, which can be simplified to
`-(2)/(7)`

Plugging that back into our equation, we have y =
`-(2)/(7)`x + b

Now, to find b, we substitute in one of our sets of coordinates. Let's use (-7, 5)

x = -7 and y = 5, which gives us:

`5 = -(2)/(7) (-7) + b`

`-(2)/(7) (-7) = 2`, which gives us:

5 = 2 + b

Subtracting 2 from both sides, we get:

3 = b

Plugging that back into our equation, we have
`y = -(2)/(7) x + 3`