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Formulas
Vocabulary
Do It
Match It
True or False
100
What is the formula for slope?
m=y2-y1/x2-x1 (Slope is also rise over run)
100
What is the difference between parallel lines and perpendicular lines?
Parallel lines are lines in the same plane that never intersect. Parallel lines have the same slope and different y-intercepts. Perpendicular lines are lines that intersect to form right angles. Perpendicular lines means that the product of their slopes is -1.
100
Write an equation given the slopes and y-intercepts. FInd the slope and y-intercepts of the equations. 1. m=9/2 b=3 2. m=8/3 b=2/3 3. y=-2x+1 4. y=x-5/4
1. y=9/2x+3 2. y=8/3x+2/3 3. m=-2 b= 1 4. m=1 b= -5/4
100
How many pairs of points do you need to calculate point-slope form?
You need one pair (x,y)
100
1. For a horizontal line, the slope is 0. 2. For a vertical line, the slope is undefined.
1. True 2. True
200
What is the formula for point-slope form?
y-y1=m(x-x1)
200
What is the negative reciprocal?
You end up with a fraction that has the opposite sign, either + or -, and the reciprocal of your original number or fraction.
200
Write an equation for the line that contains (5,1) and is parallel to y=3/5x-4
y=3/5x-2
200
In standard form, can the A or B values be negative or zero?
No. In standard form, the A and B values need to be natural numbers.
200
On a graph that graphs a horizontal line, the y value is 5. 1. The slope is 5 2. The y-intercept is 5
1. False= The slope is 0 2. True
300
What is the formula for slope-intercept form?
y=mx+b
300
In the equation y=mx+b, what does m and b stand for?
m=slope b= y=intercept (where the line crosses the y-axis)
300
Write an equation for the line that contains (0,-2) and is perpendicular to y=5x+3
y=-1/5x-2
300
Given three equations, put them into standard form. Them, match the equation to the answer. 1. y=3/5x+7 2. y=-1/3x+2 3. y=4/3x-5 a. x+3y=-6 b. 3x-5y=-35 c. 4x-3y=15
1b, 2a, 3c
300
On a graph that graphs a vertical line, the x value is 2. 1. The slope, the y value, is 0 2. The y value is none
1. False= undefined 2. True
400
What is the formula for standard form?
Ax+By=C (A and B cannot be 0 or negative)
400
What is a translation?
A translation is a shift of a graph horizontally, vertically, or both.
400
For the following equations, are they parallel, perpendicular, or neither? y=2/3x-6; y=2/3x+6 y=5x; y=-5x+7
The first one is parallel, and the second one is neither.
400
Use the point-slope form to write an equation of a line through the given points. Then match the equation to its correct answer. 1. (4,3),(-2,1) 2. (5,-4),(0,2) 3. (-1,0),(-3,-1) a. y+4=-6/5(x-5) or y-2=-6/5x b. y=1/2(x+1)=5(x-2) or y+1=1/2(x+3) c. y-3=1/3(x-4) or y-1=1/3(x+2)
1c 2a 3b
400
The equation 4x+y=9 in slope-intercept form is y=4x+9
False= y=-4x+9
500
If you are given two points, (x1,y1) and (x2,y2), what are the steps that you need to do to put it into standard form, Ax+By=C?
Slope Form= m=y2-y1/x2-x1 Point-Slope Form= y-y1=m(x-x1) Slope-Intercept Form= y=mx+b Standard Form= Ax+By=C
500
What is a parent function? What is a linear parent function?
It is the simplest equation of a function. A linear parent function is y=x or f(x).
500
Find the x- and y-intercepts of the two equations. *(Hint= To do this, must be in standard form, Ax+By+C) 1. -3x+y=6 2. 5x-3y=15
1. (-2,6) 2. (3,-5)
500
What is the slope formula useful for?
The slope formula shows you the slope,or m value in a slope-intercept form.
500
m=-3; (2,1) When using this information, when it is put into point-slope form, the answer is y-1=-3(x-2)
True