Question

Write the point-slope form of an equation of the line through the points (-7, 7) and (4, 1).

Answer 1

Choice B.
`\displaystyle y - 7 = -(6)/(11) \, (x + 7)`.

Explanation:

Start by finding the slope of this line. Let
`(x_1,\, y_1)` and
`(x_2,\, y_2)` represent two distinct points on a line on a Cartesian Plane. (That is,
`x_1 \\e x_2`.) The slope of this line would be:

`\displaystyle (y_2 - y_1)/(x_2 - x_1)`.

For the line in this question:

• 
  `x_1 = -7`,
• 
  `y_1 = 7`;

• 
  `x_2 = 4,`
• 
  `y_2 = 1`.

Indeed,
`x_1 \\e x_2`. The slope of this line would thus be
`\displaystyle (1 - 7)/(4 - (-7))`, which is equal to
`\displaystyle -(6)/(11)`.

On a Cartesian Plane, the point-slope form of a line that has a slope of
`m` and includes the point
`(x_0,\, y_0)` can be written as:

`y - y_0 = m\, (x - x_0)`.

(Note the minus signs in this form.)

For the line in this question,
`m = \displaystyle -(6)/(11)`. There are two equivalent expressions for its point-slope form:

• Using the first point,
  `y - 7 = \displaystyle -(6)/(11)\, (x - (-7))`. This equation is equivalent to
  `y - 7 = \displaystyle -(6)/(11)\, (x + 7)`.
• Using the second point,
  `y - 1 = \displaystyle -(6)/(11)\, (x - 4)`.