Forms of Slope 6 questions for 10 points. Question #1 y = mx + b is called ____________. (A) Point-slope form (B) Slope intercept form (C) Standard form.

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Presentation transcript:

Forms of Slope 6 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 Line (1)Slope-intercept form (2)Standard form (3)Point-slope form

Slope-intercept Form m = slope b = y-intercept y = mx + b

Slope-intercept Form y = mx + b What is the slope(m) and y-intercept(b) of this equation? y = 7x + 11 Since this already in the right form, m = 7 and b = 11

Slope-intercept Form y = mx + b What is the slope(m) and y-intercept(b) of this equation? y = 4/5x - 6 Since 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 + 5 Now m = 4 and the y-intercept = 5

The Harder Ones! Uh Oh! 2x – y = 10 -2x -y = -2x y = 2x + 10 x + 2y = 8 -x 2y = -x y = -1x + 4 2

WHY SLOPE- INTERCEPT FORM?

STANDARD FORM OF A LINE 4x + 8y = 16 Find the y-intercept What is x always? It is 0, so 4(0) + 8y = 16 8y = 16 y = 2 So (0, 2) 4x + 8y = 16 Find the x-intercept What is y always? It is 0, so 4x + 8(0) = 16 4x = 16 x = 4 So (4, 0)

STANDARD FORM OF A LINE PRACTICE -3x + 5y = -3 Find the y-intercept What is x always? It is 0, so -3(0) + 5y = -3 5y = -3 y = -3/5 So (0, -3/5) -3x + 5y = -3 Find the x-intercept What is y always? It is 0, so -3x + 5(0) = -3 -3x = -3 x = 1 So (1, 0)

WHY STANDARD FORM OF A LINE THIS WILL BE GREAT FOR FINDING BOTH x and y intercepts quickly

Point-Slope Form y – y 1 = m(x – x 1 ) 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, You can take any of the forms of a line and change it to another with algebra and some brains! y = 4x – 2