Answer:
The answer is
[tex]y = - \frac{5}{2} x - 1[/tex]
Step-by-step explanation:
If two equations are parallel it means that both their gradients are equal. We were given the equation:
[tex]5x + 2y = 12[/tex]
in order to find the gradient of this equation that we are given we have to ensure that it is in its simplest form:
[tex]5x + 2y = 12 \\ 2y = 12 - 5x \\ \frac{2y}{2} = \frac{12}{2} - \frac{5}{2} x \\ y = 6 - \frac{5}{2} x \: \\ or \: \\ y = - \frac{5}{2} x + 6[/tex]
Therefore the gradient of the parallel line with points (-2, 4) is also -5/2
[tex]y = mx + c \\ 4 = - \frac{ 5}{2} ( - 2) + c \\ 4 = \frac{10}{2} + c \\ 4 = 5 + c \\ 4 - 5 = c \\ [/tex]
[tex]c = - 1 \\ hence \: the \: equation \: for \: the \: \\ parallel \: line \: is \\ \: y = - \frac{5}{2} x - 1[/tex]
