2x + 3y = 7

Need help

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.