A line passes through the points (–6, 4) and (–2, 2). Which is the equation of the line? y = negative one-half x + 1 y = one-half x + 7 y = –2x – 8 y = 2x + 16

Given the points:

(-6, 4)

(-2, -2)

x1= -6

x2 = -2

y1 = 4

y2= -2

Write the equation in slope-intercept form.

Before writing the line in slope-intercept form, we equate it first in point-slope form.

Slope-intercept form:

y = mx + b

Point-slope form:

y - y1 =m(x -x1)

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 = y2 -y1 /x2 -x1

m= (-2 -4)/(-2 - (-6))

m = -6/-2 + 6

m = -6/4

m= -6/4

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

y - 4 = -6/4 ( x -(-2))
y - 4 = -6/4( x + 2)

In order to change to slope-intercept form, we distribute the value of 6/11 to the parenthesis, then transpose -4 on the other  side of the equation, hence we must take note that in transposing a number, the sign changes.

y - 4 = -6/4 ( x + 2)

y - 4 = -6/4x - 3

y = - 6/4x - 3 + 4

y= -6/4x + 1

Final answer:

y= -6/4x + 1