More Algebra Hints
Description: This lesson summaries the properties of straight lines, their slope, equations, and the slopes of perpendicular or parallel lines
5. Straight Lines
| slope m = | Dy
Dx |
= | y2-y1
x2-x1 |
= | rise
run |
Two points are usually needed to compute the slope. For a straight line segment, the slope m is a constant of proportionality between Dy = y-y1 and Dx = x-x1. The change Dy in y is proportional to the change in Dx in x.
The point-slope form of equation for a line y-y1 = m·(x-x1) implies y = y1+m·(x-x1). In the case [x1, y1] = [0, b] is the y-intercept, equation y = y1+m·(x-x1) becomes the slope intercept form of equation for a line y = b +m·x or y = m·x + b. In answering questions, rewrite any equation you obtain for a non-vertical line into a slope intercept equation. After an equation of a line is written or given in form y = m·x + b, the coefficient of x gives m and the constant term b is the y-intercept, that is the value of y when x = 0.
Graphing: Two points are usually needed to draw a straight line. Use the x- and y- intercepts if the line does not pass through the origin. For best results (greatest accuracy) in drawing a line, take two points far apart. One point is enough is the line is horizontal or vertical. Label the horizontal and vertical axises with their names and coordinates.
If L has nonzero slope m=m1 and a line K perpendicular to L has slope m2 then -1= m1·m2 . Thus m2 = -1/m1 = negative reciprocal of m1. When slope m1 of L is known, it can be used to compute the slope m2 of K without being given two points on the line K.
To find the intersection point of a line y = m1x + b1 and y = m2x + b2 , solve the equation m1x + b1 = m2x + b2 for x and then compute y.
Algebra, Odds & Ends,
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