ALGEBRA-math packet-HELP ME-equation of line!!!!???

Question

1. How would you find the equation of a line if you are only given a point such as (-2, 4) and a slope such as 3/4? (without graphing)

2. How would you find the equation of a line if you are given two points such as (1, 6) and (3, 9)? (without graphing)

3. How do you find the equation of a line if you have a point such as (-4, 3) and you know it's parallel to y=--3/4x+4? and how about if it was perpendicular?

4. How do you change it from standard form to Ax + By = C form?

Thanks you so much, this is for my Algebra II summer packet. I don't rmember how to do those things from Algebra I. I love you if you answered all or some of the questions. Thanks! MWAH!!!

Answer 1

1. plug the point(-2, 4) and the slope (3/4) into the y=mx+b format, and solve for b. (y is the y coordinate, m is the slope, x is the x coordinate, and b is the y intercept).

2. make an x-y chart with the two points:

x   y

1   6

3   9

the change in x is 2, and the change in y is 3. therefore, the slope is 3/2. then do step 1.

3. for parallel, you have the slope, and the point. do step 1. for perpendicular, take the inverse slope (in this case, -4/3), and then do step 1.

4. ax+by=c IS standard form. if you want to convert from slope-intercept (y=mx+b), move the ax over to be with the c, and divide by b.

hope this helps. best answers are always appreciated.

Answer 2

There are several different forms of the equation of the line.  They are all algebraically equivalent, so technically you only need to know one of them, but they are set up to use and supply different kinds of information, so the more of them you know, the better off you are.

In general, m is the slope.  b is the y-coordinate of the y-intercept.  The full coordinates, then, would be (0, b).  a is the x-coordinate of the x-intercept, so the full coordinates would be (a, 0).  (x, y) are variables used to indicate a general point on the line.  (x1, y1) (those should be subscripts) is a specific point on the line.

Slope-intercept form:  y = mx + b

Whatever is multiplying the x is the slope.  Whatever you're adding is the y-coordinate of the y-intercept.  So in the line y = 3x - 2, the slope would be 3 and the y-intercept would be (0, -2)

Point-slope form:  y - y1 = m(x - x1)

The slope is m, and the known point is (x1, y1).

Two-point form:  (y - y1) = [(y2 - y1)/(x2 - x1)](x - x1)

Here, as you might guess, (x1, y1) is one point and (x2, y2) is the other.

Standard or General form:  Ax + By = C or Ax + By + C = 0

Here, A, B and C are constants.  A has nothing to do with a, and B has nothing to do with B.

So:

1)  Point-slope form:  y - 4 = (3/4)(x + 2)

2)  Two-point form:  y - 6 = [(9 - 6)/(3 - 1)](x - 1)

And, of course, you have to simplify.

3)  If two lines are parallel, they have the same slope.  In this case, you know the slope of the line you want is (-3/4). Use that and the point-slope form.

If two lines are perpendicular, then their slopes are the negative reciprocals of each other.  If the slope of one, for instance, is 2/3, then the slope of the perpendicular is -3/2.  The slope of the line you want, then, is 4/3.  Use that and the point-slope form.

4)  How do you change it to what?  Just use standard algebra. For instance, if you want slope-intercept form, just solve for y:

Ax + By = C

By = -Ax + C

y = (-A/B)x + C/B