Question

​​​​​​​Which of the following equations depicts the equation of the line in slope intercept form for a line passing through (8,0) and perpendicular to a=4 b+18.

A)a= 1/4 b+7
B)a= −4b+8
C)a= 4b+18
D)a= −1/4 b+2

Answer 1

The equation of the line in slope-intercept form that passes through (8,0) and is perpendicular to the line 'a=4b+18' is 'a = -1/4b + 2', represented by answer choice D.

Step-by-step explanation:

The question is asking to find the equation of a line in slope-intercept form that passes through the point (8,0) and is perpendicular to a given line represented by 'a = 4b + 18'. To start, let's rewrite the given line in the traditional slope-intercept form, y = mx + b, where 'm' represents the slope and 'b' represents the y-intercept. Therefore, the given line becomes 'y = 4x + 18', where the slope is 4. Since we need a line perpendicular to this, we want the negative reciprocal of the slope, which is -1/4.

A line perpendicular to one with a slope of 4 will have a slope of -1/4. Using the point-slope formula, y - y1 = m(x - x1), where (x1, y1) is the point (8,0), we will insert our known values:

y - 0 = (-1/4)(x - 8)

y = -1/4x + 2

Therefore, the equation in slope-intercept form for the line passing through (8,0) and perpendicular to the original line is 'a = -1/4b + 2' which corresponds to answer choice D.