Answer:
[tex] y = \frac{-2}{5} x - 2 [/tex]
Explanation:
The general formula of the linear equation is:
y = mx + c where m is the slope and c is the y-intercept
1- getting the slope of the given line:
The given line is:
2x + 5y = 4
Rearrange to be in the general formula:
5y = -2x + 4 .............> y = [tex] \frac{-2}{5} x + 4 [/tex]
slope of the given line is : [tex] \frac{-2}{5} [/tex]
2- getting the slope of the required line:
We are given that the two lines are parallel, this means that they have equal slopes.
Therefore:
slope of the required line = [tex] \frac{-2}{5} [/tex]
The equation of the required line now became : y = [tex] \frac{-2}{5} [/tex]x + c
3- getting the value of c:
We are given that the line passes through the point (5,-4). This means that this point satisfies the equation of the line.
Therefore, we will substitute with the point in the equation and solve for c as follows:
y = [tex] \frac{-2}{5} [/tex]x + c
-4 = [tex] \frac{-2}{5} [/tex] (5) + c
-4 = -2 + c
c = -4 + 2
c = -2
Based on the above, the equation of the line is:
[tex] y = \frac{-2}{5} x - 2 [/tex]
Hope this helps :)
