desperate help with math!?

Question

1.)write an equation in standard form for the line parallel to x-2y+7=0 and contains the point (-4,0)

2.) a horizontal line intersects a vertical line at (-3,7) give the equation of each line in standard form

Answer 1

1) x-2y-4=0

Answer 2

First, get y on the left side:

x-2y+7=0
-2y=-7-x
2y=7+x
y=7/2+x/2

Two things to note:

1. The Y-intercept is 7/2
2. The slope is 1/2

Any line parallel to another has the same slope, so 1/2. Since we have a point (-4,0) we substitute these in to an equation that has 1/2 as the slope:

0=-4(1/2)+Intercept
0=-2+2

So our intercept must be -2. We combine this information:

y=2+1/2x

2. The horizontal line has a slope of 0, by definition. Also, it intersects the Y axis at 7 because it is simply a horizontal line that is equal to 7 at all x values. The vertical line only passes through the X axis for all Y values.
Horizontal line has 0 slope and Y-Intercept of 7, so:
y=7+0x=
y=7
And the vertical line is:
x=-3
Notice that for a vertical line, we don't have the form y=...because there is an infinite number of possible y values for x (and so the slope is not defined either).

Answer 3

1) x-2y+7=0
-2y=-x-7
y=1/2x+7/2

the slope is 1/2
and another point on the line is (4,0)

so you have

y=mx+b

0=1/2(4)+b
b=-2

y=1/2x-2
2y-x+2=0

2) a horizontal line that passes through (-3,7)
y=7

and the vertical line that passes through (-3,7)

x=-3

Answer 4

parallel means it has the same slope, so
x - 2y + b = 0 at (-4,0) requires that
-4 - 0 + b = 0 or that b = 4 and the equation is
x - 2y + 4 = 0

y = 7 (horizontal)
x = -3 (vertical)

HTH ☺

Doug

Answer 5

1) If parallel, then x=2y+m, so

-4=0+m, so m= -4. New equation:

x=2y-4

2) x= -3, y=7

Answer 6

1.) get into y=mx+b form
2.) plug the numbers in for x and y

Answer 7

1) y=1/2x-4
2) y=-3, x=7