Which of the following represents a horizontal line that passes through the point (2,-6)?(1) y=6(2)x=23) y = 2x - 64) y = -6x + 2​

Given:

Points ( 2, - 6)

x1 = 2

y1 = -6

Determine the equation of the line.

The equation of the line can be written in slope-intercept form, and point-slope form.

Before going to slope-intercept form, you must first determine the equation in point-slope form

Point-slope form:

y - y1 =m(x -x1)

Slope-intercept form:

y = mx + b

Solution:

Before we can write in point-slope form, we must first find the slope of the line, we can find the slope by using the slope formula.

m = y/x

m = rise over run

m = -6/2

m = -3

Substitute the given values of x1, m and y1 to the formula for the point-slope form.

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

y + 6 = 3(x - 2)

Point-slope form:
y + 6 = 3(x - 2)

To equate in slope-intercept form, we simply need to distribute 3 to each value inside the parenthesis, and then tranpsose 6 on the other side of the equation, hence it must be taken to note that in transposing numbers, the sign changes.

y + 6 = 3x - 6

y = 3x - 6 - 6

y = 3x - 12

Slope-intercept form:
y = 3x -12

Final answer:

Point-slope form:
y + 6 = 3(x - 2)

Slope-intercept form:
y = 3x -12