4.1 Identifying linear functions
Point-Slope to slope-intercept form
Parallel/Perpendicular lines
Standard Form to slope intercept form
Graphing/Miscellaneous
100
Is this a linear function?
yes
100
Write in point slope form:
slope = 4; (3, -8)
y + 8 = 4(x - 3)
100
Write another equation of a line parallel to:
y = 4x + 3
y = 4x + 1
Could have number that is different for the y-intercept but should have at least y = 4x
100
Find the x and y intercepts:
-2x + 3y = 12
x int: -6
y int: 4
100
Graph:
y=-1/3x+5
y int: 5
slope should be down 1 run right 3
200
Is this a linear function?
Not a linear function but...
Is a function called a nonlinear funciton.
200
Write in point slope form:
(8, -2) (4, -4)
y+2=1/2(x-8)
y+4=1/2(x-4)
200
Write another equation of a line perpendicular to:
y=1/3x-4
y = -3x + 4
A number works for y-int as long as y = -3x is present.
200
Write in standard form.
-4x + 7y = 14
4x - 7y = -14
200
When is the test?
Tomorrow/Thursday
January 20, 2022
01/20/22
300
Is this a linear function?
(1,2) (2,5) (3,8) (4,11) (5,14)
yes, both x and y values go up at a constant rate
300
Write in point slope and change to slope intercept form.
slope: 2; (2, 5)
y - 5 = 2(x - 2)
y = 2x + 1
300
Write the linear equation that is parallel to this line that goes through the ordered pair. Make sure answer is in slope-intercept form.
y = 3x - 5; (1, 3)
y - 3 = 3(x - 1)
y = 3x
300
Write in standard form and find the x and y intercepts.
4y = -2x - 4
Standard Form: 2x + 4y = -4
x int: -2
y int: -1
300
Graph 2x + 5y = 20
x int: 10
y int: 4
400
Which is a linear function?
Set A: (-2,5) (-1,3) (0,1) (1, -1) (2, -3)
Set B: (-1, 6), (-3, 5), (-6, 2), (-9, 1) (-12, 0)
Set A both x and y values change at a constant rate
400
Write in point slope and change to slope intercept form.
(0, 2) (2, 6)
y - 2 = 2(x - 0)
y = 2x + 2
400
Write the linear equation that is perpendicular to this line that goes through the ordered pair. Make sure answer is in slope-intercept form.
y = 4x + 6; (-4, -8)
y+8=-1/4(x+4)
y=-1/4x-9
400
Write the equation in slope intercept form and identify the slope.
-3x + 6y = 12
slope: 1/2
400
Graph:
-8y = 6x + 16
y int: -2
slope: down 3 right 4
500
Which of the following is a linear function?
y = x- 7
y = |x| - 7
y = x2 - 7
y = x - 7
500
Write in point slope and change to slope intercept form.
(6, - 5), (-2, -1)
y+1 = -1/2 (x+2)
y = -1/2x - 2
500
Write the linear equation that is perpendicular to this line that goes through the ordered pair. Make sure answer is in slope-intercept form.
y=-1/2x-2; (1,4)
y - 4 = 2(x - 1)
y = 2x + 2
500
Write the equation in slope intercept form and identify the slope.
4x + -2y = 16
slope = 2
y = 2x - 8
500
What are all three of the forms we have talked about throughout this unit and give their forms. Bonus points if you can name the 4th we talked about and can give its form.
Double Jeopardy
Standard Form: Ax + By = C
Point Slope Form: y - y1 = m(x - x1)
Slope Intercept Form: y = mx + b
Bonus: Direct Variation: y = kx