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Question 165317: what is the slope-intercept form of a linear equation?
explain why this form is called slope-intercept form?
Found 2 solutions by Earlsdon, gonzo:
Answer by Earlsdon(6294)   (Show Source):
You can put this solution on YOUR website! The "slope-intercept" form of a linear equation is expressed as:
 It is so named because you can read the slope (that's the m) and the y-intercept (that's the b) directly from the equation.
For example, in the linear equation:
 , the slope is -5 and the y-intercept is -6.
Answer by gonzo(654) (Show Source):
You can put this solution on YOUR website! slope intercept form of a linear equation is:
y = m*x + b
a linear equation is an equation of a line.
m is the slope of the line.
b is the y intercept.
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if you know 2 points on the line, you can solve for the slope.
if you already have the slope and you know one point on the line, then you can solve for the y intercept.
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here's how it works.
pick two points at random.
let point a = (x1,y1) = (5,9)
let point b = (x2,y2) = 21,5)
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formula for the slope of a line is (y2-y1) / (x2-x1).
formula for the slope of the line ab = (5-9) / (21-5)
slope of the line ab = -4 / 16 = -1/4 = -(1/4)
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you know the slope of the line ab.
call it m
m = -(1/4)
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slope intercept form of the equation for line ab is y = m*x + b
since you know the slope, this equation becomes y = -(1/4)*x + b
you now need to find the y-intercept.
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since you have the slope, all you need is one point on the line.
either of the two points will do.
take (21,5)
let x = 21
let y = 5
slope intercept form of the equation of line ab becomes 5 = -(1/4)*21 + b where b is the y-intercept.
solve for b.
multiply both sides of the equation by 4
20 = -21 + 4b
4b = 41
b = 10.25
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slope intercept form of the equation is y = -(1/4)*x + 10.25
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10.25 is the y intercept when x = 0.
all you have to do is make x = 0, and y = 10.25.
-(1/4) is the slope
graph of this equation looks like:
look below the graph for further comments.
slope intercept form of the equation for a line (linear equation) is:
y = m*x + b
in the equation for the line y = (-1/4)*x + 10.25
10.25 is the y-intercept equal the value of y when x = 0.
two points on the line ab are (5,9) and (21,5).
these are the points we used to create the equation for the line.
the horizontal lines are put there to intersect with the line at the y value of these points [ 10.25 for x = 0, 9 for x = 5, 5 for x = 21).
the slope of -1/4 means that every time x moves to the right 4 points on the graph, y moves down 1 point.
it's a little tough to see on the graph but that's what's happening.
it's probably easiest to see at the x and y axis crossing points.
those points are:
(0,10.25)
(41,0)
let (x1,y1) = (0,10.25)
let (x2,y2) = (41,0)
slope is (y2-y1) / (x1-x1)
slope = (0-10.25) / (41-0) = -10.25/41 = -1/4
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