linear π Flashcards
In mathematics, the term linear is used in two distinct senses for two different properties: linearity of a function; linearity of a polynomial. An example of a linear function is the function defined by that maps the real line to a line in the Euclidean plane RΒ² that passes through the origin.
standard form of a linear equation
ax+by=c
what is the standard form of xΒ²=-x+6?
xΒ² + x - 6 = 0
what is the difference between linear and non-linear?
linear equations donβt have exponents or square roots/cube roots etc
slope-intercept form
y=mx+b
property of m
slope/gradient
property of b or c
Y intercept
point-slope form
y β y1 = m(x β x1)
when do i use the point slope form?
to find coordinates
does function f(x) have the same property as y?
yes
identity function
f(x) = x
what is f(x) = xβs slope
1, making a 45Β°
what are parallel lines?
lines that have equal distance and never meet
what properties do parallel lines have in common?(think linear)
slope/gradient/m
Find the equation of the line that is: parallel to y = 2x + 1 and passes though the point (5,4)
y β y1 = m(x β x1)
y β 4 = 2(x β5)
y-4=2x-10
y=2x-6
what are perpendicular lines?
two lines are perpendicular when they meet at a right angle (90Β°).
to find a perpendicular slopeβ¦
use -1/m
how do i know if two lines are perpendicular?
line 1 * line 2 = -1
ND = negative
