Question

Can you break down how to solve the problem ?

Answer 1

Answer:

A.  y  = $\frac{-5x}{2}$ - 1

Step-by-step explanation:

Given parameters:

Equation of the line:

       5x + 2y = 12

Coordinates = -2, 4

Unknown:

The equation of the line parallel to this line = ?

• To solve this problem, first, we need to find the slope of the given line.

     Every linear equation have the formula:  y = mx + c

     m is the slope of the line, c is the y- intercept

           5x + 2y = 12

 Express this equation as y = mx + c

                 2y = -5x + 12

                    y = $\frac{-5}{2}x$  + 6

The slope of this line is $\frac{-5}{2}$

• Now, any line that is parallel to another will not cut or cross it at any point. This simply implies they have the same slope.

                  Slope of the line parallel is $\frac{-5}{2}$

• Our new line will also take the form y=mx + c,

          Coordinates = -2, 4, x = -2 and y = 4

                     m is $\frac{-5}{2}$

Now let us solve for C, the y-intercept;

                     4 = - 2 x $\frac{-5}{2}$  + C

                      4 = 5  + C

                       C = -1

The equation of the line is therefore;

                 y  = $\frac{-5x}{2}$ - 1