Write an equation of the line in standard form that pass through (-5,-11) and 10,7)

y = -4x/9 + 14

If this is homework, be sure to show your work.

Let's break this down into a few parts first.

Slope intercept form is otherwise known as y = mx + b, where m is the slope and b is the y-intercept.
Parallel means that the two lines will never meet. They are parallel to each other. In math terms, their slopes are the same, so the m values must be the same.

Starting with y = -5x + 1, putting into slope intercept form, y = mx + b, m = -5 and b=1.

Since it is parallel, it must have the same slope and the m values are the same.

So, y = -5x + b, but we don't know what the value of b is. To determine this, we know the point (-4,-6) is on the line that we are trying to find, so we can substitute it into the equation and calculate b to make it work.

Every time we see an x we put in -4 and every time we see a y, we put in -6.

-6 = -5(-4) + b
-6 = 20 + b
subtract 20 from both sides
-6 - 20 = 20 + b - 20
-26 = b
Now substitute this into the equation.

y = -5x + -26
Putting it into correct form, we get y = -5x - 26.

Let's check it to see if it is correct.

It has a slope of -5, so it is parallel to y=-5x + 1

Is the point (-4,-6) on the line? Let's substitute it in to see if it is on the line.

Again, everywhere we see an x, we put in -4 and everywhere we see a y we put in -6.

-6 = -5(-4) - 26
-6 = 20 - 26
-6 = -6

Sorry for the very long explanation, but after you do a few of them, you will be able to knock them off in minutes.

Good luck,

Paul

2- 4 - 8 - 16

A math teacher might know the answer to that one. Do you know a math teacher you could ask?

Assuming the 'standard form' is "slope-intercept", calculate the slope from the equation m = y2-y1 = 5 - 1 = 4 = -2
x2-x1 4 - 6 -2
The intercept can be found by substituting either of the two points into the equation y = mx + b
5 = (-2)4 + b
5 = (-8) + b
13 = b
(OR, using the other point, y = mx + b
1 = (-2)6 + b
1 = (-12) + b
13 = b )
Then expressing in general:
y = (-2) x + 13

x^2 + y^2 = 5

Being parallel to the given line, the equation of the line you are seeking has the same slope, which in this case is a=1/4.
So the equation sought is as follows
y=(1/4)x +b, where b is to be found.
To find b, use the stated fact that the line passes through the point (x=8, y=-1). All that means is that the point (8,-1) is on the line whose equation you are looking for. If it is on the line with equation y=(1/4)x+b
then its coordinates x=8, and y=-1 satisfy the relation y=(1/4)x+b. In other words, if you substitute 8 for x, and -1 for y, the equality holds true -1=(1/4)*8 +b
This gives you a way to find the initial value of the function (the y-intercept b ). Just solve -1=(1/4)*8 +b to find b.
I leave this pleasure to you.

1. Transform this equation to its functional form:
2. 9y=-3x+17 or y=(-1/3)x+17/9
3. In the last equation, the slope is the coefficient of x, namely -1/3.
   
4. A line parallel to this one must have the same slope (-1/3).
5. So the equation of your line starts this way: y=(-1/3)x+b.
6. To identify (calculate) b, you must make use of the fact that the parallel line passes through the point (1,5).
   
7. That means that the coordinates of the point (1,5) satisfy the equation of the parallel line y=(-1/3)x+b
8. Substitute 5 for y, and 1 for x and solve for b.

And that is as far I will go. I leave it to you finish up the work : find b and write the equation in the functional form, then convert it to the general form (Ax+By+C=0) if that is what you are asked to produce.

The equation of a straight line can be cast into several forms: functional form, general form, symmetrical form. The functional form is the one usually known as slope intercept form.
In the functional form, y=ax+b or sometimes y=mx+b, the factor of the x-variable (a or m as the case may be) is the slope of the straight line, and the value b, is the ordinate (y-value) of the point where the straight line cuts (intercepts) the y-axis.
Since you say nothing about the particulars of the line that interests you, there is not much more that anybody can help you with.

You are looking for a line (y=m*x+b) and have two points. From this information you can generate two equations with two unknowns (m and b are unknown).
First plug in the first point (1,5) to the general form:
5(the y value of the point) = m*1(the x-value at this point)+b
Do the same for the second point you're given.
From here solve the first equation for m in terms of b.
Plug this value of 'm' into the second equation so you will end up with something like:
3=(something in terms of b)*(-2)+b
This final equation can be solved for b (try factoring)
You now have a value for the y-intercept. Plug that into y=m*x+b
Choose either of the two points, plug into the equation on the last line with the value of b known
You then know y, x, and b and have m as the remaining 1 unknown. Solve for that and put it all together for your final answer.