Step-by-step explanation:
Q: How do I solve 2X + 3Y = 7?
The two dimensional form for the equation of a straight line is: Y = mX + b (equation 0)
where X and Y are graphic coordinates of a point on that line.
m is the slope of the line described as (Y2-Y1)/(X2-X1) where (X1,Y1) and (X2,Y2) are the coordinates of two additional distinct points on that line.
b is the point on the Y axis where the line crosses called the Y Intercept.
Back to 2X + 3Y = 7
Subtract 2X from both sides of this equation:
2X + 3Y - 2X = 7 - 2X
3Y = -2X + 7
Divide both sides of the equation 3
3Y/3 = (-2X + 7)/3
Y = -(2/3)X + 7/3 (equation 1)
Examining this equation with respect to standard form shown (equation 0), this equation (equation 1) represents a line passing through the Y axis at point location 7/3 at a dowmward to the right slope of 2/3.
To find where the line crosses the X axis (X Intercept), set Y equal to 0:
0 = -(2/3)X + 7/3
Subtracting 7/3 from both sides of the equation:
-(7/3) = -(2/3)X + 7/3 - 7/3
-7/3 = -(2/3)X
Divide both sides of the equation by -2/3
(-7/3)/(-2/3)=((-2/3)X)/(-2/3)
To divide two fractions you invert the denominator and then multiply that by the numerator.
(-7/3)*(-3/2) = (-2/3)*(-3/2)*X
21/6 = (6/6)X
7/2 = X
So drawing a line between the coordinate pairs (0,7/3) also known as (X1,Y1) and (7/2,0) also known as (X2,Y2) describes a segment of the line satisfying the initial equation.
