The required equation is 2x − 3y = 18, the correct option is D.
What is the standard equation of a line?
The standard equation of a line is given by
y = mx+c
Here m is the slope and c is the y-intercept.
The slope can be determined by
m = (y₂ -y₁)/(x₂ -x₁)
The equations are as follows:
A. 2x + 3y = −6
B. 3x − 2y = 6
C. 3x − 2y = 12
D. 2x − 3y = 18
To determine the required equation, they have to be converted to the form y=mx +c
2x +3y = -6
3y = -2x -6
y = -2/3 x - 2
Slope = -2/3
Intercept = -2
3x − 2y = 6
-2y = -3x +6
y = 3/2 x -3
Slope = 3/2
Intercept = -3
3x − 2y = 12
-2y = -3x +12
y = 3/2 x -6
Slope = 3/2
Intercept = -6
2x -3y =18
-3y = -2x +18
y = 2/3 x -6
Slope = 2/3
Intercept = -3
So, the equation that represents a line with slope 2/3 and y-intercept –6 is 2x -3y =18.
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