Question

Which of the following point-slope form equations could be produced with the points (2, -6) and (4, -3)?

y - 6 = 3/2(x + 2)
y - 6 = 3/2(x - 2)
y + 6 = 3/2(x - 2)
y + 6 = -3/2(x + 2)

Answer 1

y+6=
`\frac{\textbf{3}}{\textbf{2}}`(x-2)

Explanation:

A line passes through the points
`(2,-6)` and
`(4,-3)`.

To find the point-slope form of the line, we need a point on the line and the slope of the line.

As we have two points
`(x_(1),y_(1))` and
`(x_(2),y_(2))`, the slope can be calculated as
`(y_(2)-y_(1))/(x_(2)-x_(1))`.

Slope of the line =
`(-3-(-6))/(4-2)=(3)/(2)`

Given a line with slope
`m` and a point
`(x_(1),y_(1))`, slope-point form is
`y-y_(1)=m(x-x_(1))`

Line is given by
`y+6=(3)/(2)(x-2)`

∴ The line is given by
`y+6=(3)/(2)(x-2)`