a. The standard form of an equation of a line is ___________, where A and B are not both zero and C is a constant. b. A line defined by an equation y = k , where k is a constant is a (horizontal/vertical) line. c. A line defined by an equation x = k , where k is a constant is a (horizontal/vertical) line. d. Given the slope-intercept form of an equation of a line, y = m x + b , the value of m is the ________ and b is the _________. e. Given a point ( x 1 , y 1 ) on a line with slope m, the point-slope formula is given by _________.
a. The standard form of an equation of a line is ___________, where A and B are not both zero and C is a constant. b. A line defined by an equation y = k , where k is a constant is a (horizontal/vertical) line. c. A line defined by an equation x = k , where k is a constant is a (horizontal/vertical) line. d. Given the slope-intercept form of an equation of a line, y = m x + b , the value of m is the ________ and b is the _________. e. Given a point ( x 1 , y 1 ) on a line with slope m, the point-slope formula is given by _________.
Solution Summary: The author explains how the standard form of an equation of a line is underset_Ax+By=C — where A and B are non-zero and
a. The standard form of an equation of a line is ___________, where A and B are not both zero and C is a constant.
b. A line defined by an equation
y
=
k
, where k is a constant is a (horizontal/vertical) line.
c. A line defined by an equation
x
=
k
, where k is a constant is a (horizontal/vertical) line.
d. Given the slope-intercept form of an equation of a line,
y
=
m
x
+
b
, the value of m is the ________ and b is the _________.
e. Given a point
(
x
1
,
y
1
)
on a line with slope m, the point-slope formula is given by _________.
Formula Formula Point-slope equation: The point-slope equation of a line passing through the point (x 1 , y 1 ) with slope m , is given by the following formula: y - y 1 = m x - x 1 Example: The point-slope equation of a line passing through (2, -6) with slope 5 is given by: y - (-6) = 5(x - 2) y + 6 = 5(x - 2)
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ANALYZING RELATIONSHIPS Describe the x-values for which (a) f is increasing or decreasing, (b) f(x) > 0 and (c) f(x) <0.
y Af
-2
1
2 4x
a. The function is increasing when
and
decreasing when
By forming the augmented matrix corresponding to this system of equations and usingGaussian elimination, find the values of t and u that imply the system:(i) is inconsistent.(ii) has infinitely many solutions.(iii) has a unique solutiona=2 b=1
if a=2 and b=1
1) Calculate 49(B-1)2+7B−1AT+7ATB−1+(AT)2
2)Find a matrix C such that (B − 2C)-1=A
3) Find a non-diagonal matrix E ̸= B such that det(AB) = det(AE)
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