Forms for the equation of a straight line
Suppose that we have the graph of a straight line and that we wish to find its equation. (We will assume that the graph has x and y axes and a linear scale.) The equation can be expressed in several possible forms. To find the equation of the straight line in any form we must be given either:
two points, (x1, y1) and (x2, y2), on the line; or
one point, (x1, y1), on the line and the slope, m; or
the y intercept, b, and the slope, m.
In the first case where we are given two points, we can find m by using the formula:
Once we have one form we can easily get any of the other forms from it using simple algebraic manipulations. Here are the forms:
1. The slope-intercept form:
y = m x + b.
The constant b is simply the y intercept of the line, found by inspection. The constant m is the slope, found by picking any two points (x1, y1) and (x2, y2) on the line and using the formula:
2. The point-slope form:
y − y1 = m (x − x1).
(x1, y1) is a point on the line. The slope m can be found from a second point, (x2, y2), and using the formula:
3. The general form:
a x + b y + c = 0.
a, b and c are constants. This form is usually gotten by manipulating one of the previous two forms. Note that any one of the constants can be made equal to 1 by dividing the equation through by that constant.
4. The parametric form:
1. C
2. A
3. B
Hope This Helped!
<u><em>(Brainliest will be appreciated)</em></u>
4x=x
IS that what it is wanting? I don't quite know. If I am correct I am glad I could help but If I am incorrect then I very very very very sorry!
<h3>
Answer:</h3>
(2x + 1)(x + 3)
<h3>
Step-by-step explanation:</h3>
It is probably easier to try the answer choices than to try to factor the expression yourself.
(2x + 2)(x + 1) = 2x² +4x +2
(2x + 3)(x + 1) = 2x² +5x +3
(2x + 1)(x + 3) = 2x² +7x +3 . . . . . correct choice
_____
<em>Constructed solution</em>
If you want to factor this yourself, you can look for factors of "ac" that add to give "b". That is, you want factors of 2·3 = 6 that add up to give 7. You don't have to look very far.
... 6 = 1·6 = 2·3 . . . . . . the first factor pair adds to give 7
Now, rewrite the x term using the sum of these numbers.
... 2x² +(1 +6)x +3
... 2x +x +6x +3 . . . . eliminate parentheses
... (2x +x) +(6x +3) . . . . group pairs of terms
... x(2x +1) +3(2x +1) . . . . factor each pair
... (x +3)(2x +1) . . . . . . matches the last selection
