Standard form?

I don't know how to use standard form. The formula for it is


ax+by=c


I have to solve 2 problems using it.


A horizontal line intersects with a vertical line as (-3,7). Give the equation of each line in standard form.


What are all the steps?





Write an equation in standard form for the line parallel to


x-2y+7=0 and contains the point (-4,0).





Please help me with both of these. I need to show all steps and please explain.

Standard form?
Any horizontal line will be y = number. As you want it to intersect another at (-3, 7) it must be y = 7. This is in standard form. Remember that any of a, b, c can be zero (or one which you don't write in).





Lines which are parallel differ only in the c number so for your second one you want a line parallel to x - 2y = -7 so it will be


x - 2y = number. I'll leave you to find the number knowing that


x = -4, y = 0 must make the equation correct.
Reply:A horizontal line intersects with a vertical line as (-3,7). Give the equation of each line in standard form.


What are all the steps?








Both lines go through the point (-3,7)


where x = -3, the equation is the vertical line is x=-3


where y= 7, the equation is the horizontal line is y=7


--------------------------------------...


Write an equation in standard form for the line parallel to


x-2y+7=0 and contains the point (-4,0).





-2y=-x-7


y=1/2 x +7/2


so the slope you need is 1/2





y=1/2x+b


0=1/2(-4)+b


0=-2+b


2=b





y=1/2 x+2


2y=x+4


-x+2y=4


x-2x=-4
Reply:A linear equation in the standard form is Ax + By + C = 0, where A, B and C are integers, while A%26gt;0





A horzontal line has the form y = a, where a is a real number. i.e, everywhere on this line y has the same value of a, no matter what value of x you pick.





If a horizontal line intersects another line at (-3, 7), then the horiz. must have the equation y = 7.


or, In the standard form, 0x + 1y -7 = 0.





The other line is vertical, that means it has the same x value everywhere, no matter what y value you pick. So the equation of the vertical line must be x = -3, as it passes through x = -3.


In the standard form, x + 0y +3 = 0.





The Secomd Problem:


Two parallel lines have the same slope. So the key here is to find the slope of the given line. The given line is in the standard form, we have to re-arrange that in the slope-intercept form. i.e., y = (1/2 x) + (7/2)


This implies that both lines will have the slope of 1/2, as both are parallel.





So the equation for the new line could be written as


y = (1/2 x) + b. To find b, plug in the coordinates (-4, 0) in the equation. This gives 0 = -2 + b; or, b = 2


So the equation for the new line is y = 1/2x + 2. We need to write that in the standard form. Since only integer coefficients are allowed, let us multiply both sides by 2:


2y = x + 4


Re-arrange to the standard form:


x -2y + 4 = 0.


That is all.

avender