A2x - 6y = 12
B3x - 2y = 12
C2x - 5y = 6
D2x - 3y = 12
Answer:
D. 2x - 3y = 12
Read Explanation:
Equation of a Line
The general equation of a straight line can be represented in various forms. For this problem, we utilize the point-slope form and the slope-intercept form, and then convert it to the standard form (Ax + By = C).
Point-Slope Form
The point-slope form of a linear equation is given by: y - y1 = m(x - x1)
Here, m represents the slope of the line, and (x1, y1) is a point that the line passes through.
Given Information
Slope (m) = 2/3
Point (x1, y1) = (3, -2)
Applying the Point-Slope Form
Substitute the given values into the point-slope formula:
y - (-2) = (2/3)(x - 3)
Simplify the equation:
y + 2 = (2/3)(x - 3)
Converting to Standard Form (Ax + By = C)
To eliminate the fraction, multiply both sides of the equation by 3:
3(y + 2) = 2(x - 3)
Distribute the constants:
3y + 6 = 2x - 6
Rearrange the terms to match the standard form. Move the 'x' term to the left and the constant term to the right:
-2x + 3y = -6 - 6
-2x + 3y = -12
Multiply the entire equation by -1 to make the coefficient of 'x' positive, which is a common convention for the standard form:
2x - 3y = 12
Alternative Method: Slope-Intercept Form
The slope-intercept form is y = mx + c, where 'c' is the y-intercept.
Substitute the slope (m = 2/3):
y = (2/3)x + c
Use the given point (3, -2) to solve for 'c':
-2 = (2/3)(3) + c
-2 = 2 + c
c = -2 - 2
c = -4
Now, substitute 'c' back into the slope-intercept form:
y = (2/3)x - 4
Convert this to the standard form (Ax + By = C) as done previously. Multiply by 3:
3y = 2x - 12
Rearrange:
-2x + 3y = -12
Multiply by -1:
2x - 3y = 12