Answer:
A. Slope = -³/2
B. y = -³/2x - 6
C. ³/2x + y = -6
Explanation:
A. Slope of the line would be the negative reciprocal of the slope of 2x - 3y = 12, which is written in standard form. Rewrite in slope-intercept form, y = mx + b, where m = slope.
Thus:
2x - 3y = 12
-3y = -2x + 12
y = -2x/-3 + 12/-3
y = ⅔x - 4
The slope of 2x - 3y = 12 is therefore ⅔.
The slope of the line perpendicular to 2x - 3y = 12 would be the negative reciprocal of its slope, ⅔ which is:
-³/2
Therefore, the slope of the line perpendicular to 2x - 3y = 12 is -³/2
B. To find the equation of the line in slope-intercept form, first find the equation in point-slope form using the point given (-6, 3) and slope of the line, -³/2.
Substitute a = -6, b = 3, and m = -³/2 into y - b = m(x - a).
Thus:
y - 3 = -³/2(x - (-6))
y - 3 = -³/2(x + 6)
Rewrite in slope-intercept form, y = mx + b
Multiply both sides by 2
2(y - 3) = -3(x + 6)
2y - 6 = -3x - 18
2y = -3x - 18 + 6
2y = -3x - 12
y = -3x/2 - 12/2
y = -³/2x - 6
C. Rewrite y = -³/2x - 6 in standard form.
y = -³/2x - 6
³/2x + y = -6