Question

What is an equation of the line that passes through the points (4,-6) and has a slope of -3

1) y = -3x + 6
2)y = -3x - 6
3)y = -3x + 10
4) y = -3x + 14

Answer 1

1) y = -3x + 6

Explanation:

1) First, write the equation of the line in point-slope form with the given information. Use the point-slope formula
`y-y_1 = m (x-x_1)` and substitute values for
`m`,
`x_1`, and
`y_1`.

Since
`m` represents the slope, substitute -3 in its place. Since
`x_1` and
`y_1` represent the x and y values of the point the line intersects, substitute the x and y values of (4,-6) into the formula as well. This gives the following equation:

`y+6 = -3(x-4)`

2) Now, isolate the y in the equation to put it in slope-intercept form and find the answer.

`y + 6 = -3(x-4)\\y + 6 = -3x+12\\y = -3x+6`

So, the first option is correct.