Question

What is the equation of the line that is parallel to the line 5x 2y = 12 and passes through the point (−2, 4)? y = – five-halvesx – 1 y = – five-halvesx 5 y = two-fifthsx – 1 y = two-fifthsx 5

Answer 1

Answer:

The answer is

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

Step-by-step explanation:

If two equations are parallel it means that both their gradients are equal. We were given the equation:

$5x + 2y = 12$

in order to find the gradient of this equation that we are given we have to ensure that it is in its simplest form:

$5x + 2y = 12 \\ 2y = 12 - 5x \\ \frac{2y}{2} = \frac{12}{2} - \frac{5}{2} x \\ y = 6 - \frac{5}{2} x \: \\ or \: \\ y = - \frac{5}{2} x + 6$

Therefore the gradient of the parallel line with points (-2, 4) is also -5/2

$y = mx + c \\ 4 = - \frac{ 5}{2} ( - 2) + c \\ 4 = \frac{10}{2} + c \\ 4 = 5 + c \\ 4 - 5 = c$

$c = - 1 \\ hence \: the \: equation \: for \: the \: \\ parallel \: line \: is \\ \: y = - \frac{5}{2} x - 1$