please someone help with these equations please please i have been racking my brain forever and i suck at this

Question

#1.write the equation of the line perpendicular to x+7y-12=0 and passing through point (5,-9)
#2. write the equation of the line with slope -9 passing through (4,3)
#3. can someone tell me how i would graph x=2? where would i put my points???

Answer 1

#1 Firstly you need to know what that y=mx+c is the general Linear Equation.
where m is the gradient if a line is perpendicular to another line it means they have inverse gradients (i.e. swap the signs around so neg becomes pos and positive becomes neg)

so first you need to work out 'm' to do this you need to write the eqn in the format of y=mx+c

x + 7y - 12 = 0
x + 7y = 12
7y = 12 - x
y = (12 - x)/7
y = -1/7 x + 12/7
in this case your m= -1/7
and now you just need to substitute your point (5,-9) back into the equation

y=-1/7 x + c and solve for c


#2 This is a linear function which is given by y=mx+c
where m is the gradient/slope

so you have m=-9
sub it in and get
y = -9x + c
you have coordinates so sub in coordinates (4,3) and solve for c and you get your linear eqn

#3 well if you have a x-y graph. Think about it, for every value of y, x will always be 2. That means at y=0,x=2 at y=1,x=2 at y=10,x=2 at y=134314314,x=2 etc

Answer 2

OK, here is my shot at #1. The general equation for a line is y=mx+b, where m is the slope and b is the y-intercept point (the value of x when y=0). We need to get the equation you were given into that form.
x+7y-12=0
x+7y=12
7y=(-1)x+12
y=(-1/7)x+12/7

Sothe given equation has a slope of (-1/7). A perpendicular line will have a slope that is the additive inverse, meaning the number that is (-1) times it, so the slope of the line you want is 1/7.

Now you need to find the line's y-intercept. We use the given point, (5,-9), and the slope 1/7, in the general line equation.

y=mx+b
-9=(1/7)*5+b
-9=5/7+b
(-9 5/7)=b

So the y-intercept is -9 5/7, making the line's equation

y= (1/7)x -(9 5/7)

Answer 3

#1: when a line is perpindicular, its slope will be -1/m where m equals the slope of the original line. Therefore:
x + 7y - 12 = 0
Change into y = mx+b form where m = slope
7y = -1x + 12
y = (-1/7)x + 12/7
put (-1/7) into perpindicular slope formula to get the slope:
m = -1 / (-1/7) = 7
Input the given point (5, -9) in the y = mx + b formula to find y intercept:
-9 = 7(5) + b
b = -44
The equation is therefore: y = 7x - 44 or 7x - y - 44 = 0

#2: Again, y = mx + b
3 = -9(4) + b
b = 39
equation is y = -9x + 39

#3: to graph x = 2, draw a vertical line at x = 2. Sample points could be (2, 1), (2, 0), (2, -1), and anything else you want as long as x = 2.

Answer 4

Question 1
7y = - x + 12
y = (-1/7) x + 12/7
Given line thus has gradient = -1/7
Gradient of perpendicular line is then 7
Equation of perpendicular line passing thro` (5 , - 9) is given by:-
y - (-9) = 7 (x - 5)
y + 9 = 7x - 35
y = 7x - 44

Question 2
y - 3 = - 9(x - 4)
y - 3 = -9x + 36
y = -9x + 39

Question 3
The line x = 3 is a line parallel to the y axis that passes thro` point (3,0)

Answer 5

#1 -- IDK
#2 -- IDK
#3 -- A line going vertical crossing the x-axis at x=2.