Linear Functions
Does this equation represent a linear function?
Yes or No
2x + 3y = 5
Yes
What is the equation look like for Standard Form?
Ax + By = C
What does the slope formula look like?
(y2 - y1) / (x2 - x1)
What does the equation for Slope-Intercept Form look like?
y = mx + b
What does the equation for Point-Slope Form look like?
y - y1 = m (x - x1)
Do the given ordered pairs satisfy a linear function? Explain
(0,5) (-2, 3) (-4, 1) (-6, -1) (-8, -3)
Yes, this is a function because the pattern in the x-coordinates is -2 and the pattern for the y-coordinates is also -2.
What is the x-intercept and y-intercept of the equation?
2x - 4y = 4
x-int. = 2
y-int. = -1
What is the slope of a vertical line?
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Write the equation that describes the line in Slope-Intercept Form.
slope = 5 and the y-intercept = -9
y = 5x - 9
Write an equation in Point-Slope Form for the line with the given slope and the given point.
slope = 1/5 and the point is (2,-6)
y + 6 = 1/5 (x - 2)
Tell whether the given ordered pairs satisfy a linear function. Why or why not?
(2, -2) (-1, 0) (-4, 1) (-7, 3) (-10, 6)
No this is not a linear function because the pattern for the y-coordinates is not consistent.
Write the equation in Standard Form.
4y + 5x = 2y - 3x + 16
8x + 2y = 16
Find the slope of the line that passes through the points (2,7) and (4,4).
-3/2
Write the equation in Slope-Intercept Form.
6x + 3y = 12
y = -2x + 4
Write an equation in Point-Slope Form for the line with the given slope and the given point.
slope = -6 and the point is (-8, -10)
y + 10 = -6 (x + 8)
Is this function linear? Why or why not?
x^2 + 3 = y
No, this is not a linear function because the variable x has a power of 2.
What is the x-intercept and y-intercept of the equation?
y - 3x = -15
x-int. = 5
y-int. = -15
Find the slope of the line that contains the pair of points.
(2,5) and (3,1)
-4
Write the equation that describes the line in Slope-Intercept Form.
slope = 0 and (6, -8) is on the line
y = -8
Write an equation in Point-Slope Form for the line that goes through these two points.
(1, 1) and (-5, 3)
y - 3 = -1/3 (x + 5)
y - 1 = -1/3 (x - 1)
Is this function linear? Why or why not?
x/5 = y/3
Yes, this is a linear function. The variables are in the top of the fractions and have a power of 1.
What is the x-intercept and y-intercept of the equation?
-2y + x = 2y - 8
x-int. = -8
y-int. = 2
Find the slope of the line described by the equation.
8x + 2y = 96
-4
Write the equation in Slope-Intercept Form.
5x - 2y + 6 = 10
y = 5/2 x - 2
First write an equation in Point-Slope Form for the given information AND then write it in Slope-Intercept Form.
slope = 2 and the line goes through (3, 4)
y - 4 = 2 (x - 3)
y = 2x - 2