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Linear Equations
Slope-Intercept Form
• Standard-form – an equation of a line in the form Ax + By + C
• Value of A is greater than or equal to 0
• Value of A and B are not both 0
• Value of A, B, and C are real number constants
• Ex) 3x + 2y = 6
• Subtract 3x from both sides of equation, 2y = –3x + 6
!!!
• Then, divide both sides of equation by 2 for 𝑦 = ! + 3
• Lines can be graphed by identifying the transformations on the linear
parent function, y = x
!!!
• Ex) 𝑦 =
+3
!
• Reflected over the y-axis
• Vertically stretched
• Vertically translated up the y-axis by 3
• (0,3) is the y-intercept
• Slope is –3/2
Slope-intercept form of a line
• Advantages of slope-intercept form
• Equation can be written quickly if slope and y-intercept are
The slope-intercept form of an
known
equation of a line is in the form
• Slope and y-intercept recognized immediately in equation
y = mx + b
where m is the slope of the line, and b
and line can be graphed quickly
is the y-intercept.
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Algebra II 2.4 Linear Equations
Linear Equations
Point-Slope Form
Point-slope form of a line
• When a slope is given without a y-intercept, an equation can be formed
from a point on the line
• Must apply transformations to the linear parent function
• Ex) If slope is 1/2, then the graph should be vertically
!
compressed, 𝑦 = ! 𝑥
• If the point on the line is (4,5), then translate to the right by
!
four units and up by five units, 𝑦 = 𝑥 − 4 + 5
!
The point-slope form of the
equation of a line is
y – y1 = m(x – x1)
where m is the slope of the line,
and (x1,y1) is a point on the line.
!
• Value of y can be moved to the other side, 𝑦 − 5 = ! (𝑥 − 4)
• Advantages of point-slope form
• Equation can be formed quickly from the slope and one point of a line
• Can find y-intercept by solving the equation for y and converting the equation
into slope-intercept form
Horizontal & Vertical Lines
• Sometimes linear equations do not appear to contain both x- and y-components
• Ex) y = 4
• Two points on the line are (–3,4) and (5,4)
! !!
!!!
!
• Slope is !! !!! = !!(!!) = ! = 0
!
!
• Slope–intercept form is y = 0x + 4, point–slope equation is y – 4 = 0(x – 5)
• Ex) x = 4
• Two points on the line are (4, –2) and (4,3)
• Slope is
!! !!!
!! !!!
=
!!(!!)
!!!
!
= = undefined
!
• Impossible to write equation of a vertical line in slope–intercept or
point–slope form
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Algebra II 2.4 Linear Equations