If the lines 4x-y+2=0 and x+2ky+1=0 are perpendicular to each other, determine the value of k

For a line in the general form,
,

so

and

we require that

therefore...

so

Write the given equation in point-slope form

Find the equation a the line that passes P(3,2) and Q(3,-4)

x values are constant ==> vertical line 
x=3

Do the equations x = 4y + 1 and x = 4y – 1 have the same solution? How can I explain this to someone that does not know algebra?

No. The solution of a linear function in two variables is an infinite set of points - so we typically represent it as a graph, or we may talk about particular solutions. For example what is x when y=0?

Graphing each of these equations we will get two different lines - that's one sure-fire way to know they have different solutions.

:)

What is the slope and equation of a line perpendicular to x=6 through (-3,-7)

a line perpendicular to a vertical line has a slope of m=0, So we know y=-7

What is the equation of a line that has a slope of 7/9 and contains the point (0,6) ?

using point-slope equation:
y-6=7/9 (x-0)

Find an equation of the line through the given points. Write the equation in standard form. Through (-1,1) and (1, -13).

m=(-13-1)/(1-(-1))=-14/2=-7
y-1=-7(x-(-1))
y-1=-7x-7
7x+y=-6

Write the following equations in slope-intercept form. 5x + y = 30

To put this equation in slope-intercept form all we need to do is solve for x and list the x-term first:

 

What is an equation of the line that passes through the point (3,1) and is perpendicular to the line x+2y=14. (In point-slope form)

m=-1/2
so
mperp=2
y-1=2(x-3)

Write the equation of the line in general form

Find the slope

Slope-Intercept form

Write the equation of the line in general form

Find x and y intercepts of the graph y=-3

This is a horizontal line so no x-intercept and y-intercept: (0,-3)

Find x and y intercepts of the graph x=-1

This is a vertical line so no y-intercept, x-intercept: (-1,0)

What is the equation of the line with the given ordered pairs of (3,5) and (9,7)

(3,5) and (9,7)
leads to 
 

Then
using (3,5)

becomes

Write an equation of the line that passes through the point P and is parallel to the line with the given equation: P(-1,3); y = -4x + 7

P(-1,3); y = -4x + 7 
tells us m=-4 and so 
y-3=-4(x+1) 


:)

Indicate in standard form the equation of the line passing through the given points. X(0, 6), Y(5, 6)

y-coordinates do not change so this line has m=0 (horizontal line)
Therefore y=6

Find the equation of the line through two points

If (5, -3) is a known solution of 4x+by=29, find b