Question

Write the polnt-slope form of the equation of the line passing through the points (-5, 6) and (0, 1).

y- 6 = 1(x + 5)
y+6= -1(x - 5)
y- 6 = -1(x + 5)
y+ 6 = 1(x - 5)

Answer 1

y - 6 = -1 (x+5)

Explanation:

1) First, find the slope of the line. Use the slope formula
`m = (y_2-y_1)/(x_2-x_1) \\`. Substitute the x and y values of (-5,6) and (0,1) into the formula and simplify like so:

`m = ((1)-(6))/((0)-(-5)) \\m = (1-6)/(0+5) \\m = (-5)/(5) \\m = -1`

So, the slope of the line is -1.

2) Now we have enough information to write the equation of the line in point-slope form. Use the point-slope formula
`y-y_1 = m (x-x_1)` and substitute real values for the
`m`,
`x_1`, and
`y_1`.

Since
`m` represents the slope of the line, substitute -1 in its place. Since
`x_1` and
`y_1` represent the x and y values of a point the line intersects, substitute the x and y values of (-5, 6) in those places as well. This gives the following equation and answer:

`y-6 = -1(x+5)`