Write an equation of the line parallel to x+2y=-4 through the point (-8,5) show all work

The equation of the parallel line would be y = -1/2x + 1

Step-by-step explanation:

To start we need to find the slope of the original  line. We can do that by solving for y.

x + 2y = -4

2y = -x - 4

y = -1/2x - 2

Since the slope of the original line is -1/2 and parallel lines have the same slope, we know the new line will also have -1/2 slope. Now we can use that along with the point given in point-slope form to get the find equation.

y - y1 = m(x - x1)

y - 5 = -1/2(x + 8)

y - 5 = -1/2x - 4

y = -1/2x + 1

p ÷ r = tan(x)

step-by-step explanation:

given that there is a figure below shows a right triangle: a right triangle is shown with hypotenuse equal to q units and the length of the legs equal to p units and r units.

graph is missing so i will create the graph as per given information.

the angle between the legs having lengths p units and q units is y degrees. the angle between the legs having lengths r units and q units is x degrees.

now we need to find about what is p ÷ r equal to.

so we can use trigonometric ratio tan(x)=[altitude]/[base] to find the value of p ÷ r, because p is the altitude and r is the base.

p ÷ r=tan(x)

hence final answer is p ÷ r=tan(x).