forms of slope 6 questions for 10 points. question #1 y = mx + b is called ____________. (a)...
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Forms of SlopeForms of SlopeForms of SlopeForms of Slope
6 questions for 10 points6 questions for 10 points
Question #1•y = mx + b is called ____________.
•(A) Point-slope form•(B) Slope intercept form•(C) Standard form
Question #2•Ax + By = C is called ___________.
•(A) Point-slope form•(B) Slope intercept form•(C) Standard form
Question #3•Which form is easiest to
use when finding the x-intercept of an equation?
•(A) Point-slope form•(B) Slope intercept form•(C) Standard form
Question #4•Which form DOES NOT have an m(slope)?
•(A) Point-slope form•(B) Slope intercept form•(C) Standard form
Question #5• Which form COULD look
like this: y + 3 = -4(x – 5)
•(A) Point-slope form•(B) Slope intercept form•(C) Standard form
Question #6•Given, y = 2x – 7, the -7 represents the ______.
•(A) y-intercept•(B) slope•(C) both A and B
Forms of a LineForms of a LineForms of a LineForms of a Line
(1)(1)Slope-intercept formSlope-intercept form
(2)(2)Standard formStandard form
(3)(3)Point-slope formPoint-slope form
Slope-intercept Form
•m = slope•b = y-intercept
y = mx + b
Slope-intercept Formy = mx + b
What is the slope(m) and y-intercept(b) of this equation?
y = 7x + 11Since this already in the right form, m = 7 and b = 11
Slope-intercept Formy = mx + b
What is the slope(m) and y-intercept(b) of this equation?
y = 4/5x - 6Since this already in the right form, m = 4/5 and b = -6
the “y” term is all by itself on the left side of the equation.That is very important!
WHY?If the “y” is not all by itself, then we must first use the rules of algebra to isolate the “y” term.
For example in the equation:
2y = 8x + 10
You will notice that in order to get “y” all by itself we have to divide both sides by 2.
After you have done that, the equation becomes:
y = 4x + 5Now m = 4 and the y-intercept = 5
The Harder Ones! Uh Oh!
2x – y = 10-2x -2x-y = -2x + 10-1 -1 -1y = 2x + 10
x + 2y = 8-x -x2y = -x + 8 2 2 2y = -1x + 4 2
WHY SLOPE-INTERCEPT FORM?
STANDARD FORM OF A LINE
4x + 8y = 16Find the y-interceptWhat is x always?It is 0, so4(0) + 8y = 168y = 16y = 2So (0, 2)
4x + 8y = 16Find the x-interceptWhat is y always?It is 0, so4x + 8(0) = 164x = 16x = 4So (4, 0)
STANDARD FORM OF A LINE PRACTICE
-3x + 5y = -3Find the y-interceptWhat is x always?It is 0, so-3(0) + 5y = -35y = -3y = -3/5So (0, -3/5)
-3x + 5y = -3Find the x-interceptWhat is y always?It is 0, so-3x + 5(0) = -3-3x = -3x = 1So (1, 0)
WHY STANDARD WHY STANDARD FORM OF A LINEFORM OF A LINEWHY STANDARD WHY STANDARD FORM OF A LINEFORM OF A LINETHIS WILL BE GREAT FOR THIS WILL BE GREAT FOR
FINDING BOTH x and y FINDING BOTH x and y intercepts quicklyintercepts quickly
Point-Slope Formy – y1 = m(x – x1)
Given one point and the slope, you can graph the point and use the slope to determine a second point to
graph.
y – 1 = ⅘(x – 3)
The point would be (3, 1) and the slope would be ⅘.Note: Point-Slope Form is negative!!!!!!!!!!Plot (3,1) rise 4 and run 5 to the point(8,5)
y – 4 = -3(x – 1)
IN CLOSING, IN CLOSING, You can take any of the forms of a You can take any of the forms of a line and change it to another with line and change it to another with
algebra and some brains!algebra and some brains!
IN CLOSING, IN CLOSING, You can take any of the forms of a You can take any of the forms of a line and change it to another with line and change it to another with
algebra and some brains!algebra and some brains!
y = 4x – 2 y = 4x – 2