Using the slope-intercept form: y = m*x + b |
Using the slope-intercept form: y = a + b*x |
Situation 1: Find the equation of a line if we are told that the slope is ¾ and the y-intercept is at the point (0,5). | |
We have the y-intercept form as y = m*x + b, where
m is the slope and b is the second coordinate of the y-intercept.
But we told that m is ¾ and the y-intercept is the point
(0,5), which means that b is 5.
Therefore, our equation is
|
We have the y-intercept form as y = a + b*x, where
a is the second coordinate of the y-intercept and
b is the slope.
But we told that b is ¾ and the y-intercept is the point
(0,5), which means that a is 5.
Therefore, our equation is
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Situation 2: Find the equation of a line if we are told that the slope is 2.5 and the the line contains the point (4,7). | |
We have the y-intercept form as y = m*x + b, where
m is the slope and b is the second coordinate of the y-intercept.
But we told that m is 2.5.
However, we have no idea about the value of the y-intercept.
We can at least start writing the equation of the line as
|
We have the y-intercept form as y = a + b*x, where
a is the second coordinate of the y-intercept and
b is the slope.
But we told that b is 2.5.
However, we have no idea about the value of the y-intercept.
We can at least start writing the equation of the line as
|
Situation 3: Find the equation of a line if we are told that y-intercept is (0,2) the line contains the point (6,-7). | |
We have the y-intercept form as y = m*x + b, where
m is the slope and b is the second coordinate of the y-intercept.
But we told that b is 2.
However, we have no idea about the value of the slope.
We can at least start writing the equation of the line as
|
We have the y-intercept form as y = a + b*x, where
a is the second coordinate of the y-intercept and
b is the slope.
But we told that a is 2.
However, we have no idea about the value of the slope.
We can at least start writing the equation of the line as
|
Situation 4: Find the equation of a line if we are told that the line contains the point (-4,-2) and the point (8,-5). | |
We have the y-intercept form as y = m*x + b, where
m is the slope and b is the second coordinate of the y-intercept.
However, we have no idea about the value of the either the slope or the y-intercept.
We do know two points on the line. If we say that point 1 is
(x1,y1) = (8,-5) and
that point 2 is
(x2,y2) = (-4,-2) then
we can compute the slope of the line containing those two points as m =
y2 − y1
/
x2 − x1
=
-5 − (-2)
/
8 − (-4)
=
-3
/
12
=
-1
/
4
. Now we know that m=(-1/4).
We can at least start writing the equation of the line as
|
We have the y-intercept form as y = a + b*x, where
a is the second coordinate of the y-intercept and
b is the slope.
However, we have no idea about the value of the either the slope or the y-intercept.
We do know two points on the line. If we say that point 1 is
(x1,y1) = (8,-5) and
that point 2 is
(x2,y2) = (-4,-2) then
we can compute the slope of the line containing those two points as b =
y2 − y1
/
x2 − x1
=
-5 − (-2)
/
8 − (-4)
=
-3
/
12
=
-1
/
4
. Now we know that b=(-1/4).
|