Enter the correct answer in the box. consider the system of equations. 3x + 2y = 23 1/2x - y = 4 rewrite the first equation in slope-intercept form to find an expression that can be substituted for y in the second equation.

Slope-intercept form:  y = (-3/2)x + 11.5

Step-by-step explanation:

The first equation, 3x + 2y = 23, is in the standard form of a function ( Ax + By = C).  In order to convert to slope-intercept form (y = mx + b), you can use the standard form equation and simply solve for the variable 'y'.  Using inverse operations to isolate the variable, we would first subtract '3x' from both sides of the equation:  3x - 3x + 2y = 23 - 3x or 2y = -3x + 23.  Next, we need to divide all terms by 2 in order to get rid of the coefficent in front of 'y':  2y/2 = (-3/2) x + (23/2) or y = (-3/2)x + 11.5.  You can then use this expression of 'y' to substitute for the value of 'y' in the second equation.  

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below:

.there can be infinite values of m and n that can satisfy the above equation. for each value of m of m or n. there maybe infinite sets of solution for the above

step-by-step explanation: