advanced algebra 1. slope-intercept form point-slope form
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Chapter 4 ReivewAdvanced Algebra 1Various Forms of an Equation of a Line.Slope-Intercept FormPoint-Slope Form
Lets try one
Given m (the slope remember!) = 2And b (the y-intercept) = (0, 9)All you have to do is plug those values intoy = mx + bThe equation becomesy = 2x + 9Write the equation of a line after you are given the slope and y-interceptGiven m = 2/3, b = -12,Write the equation of a line in slope-intercept form.Y = mx + bY = 2/3x 12*************************One last exampleGiven m = -5, b = -1Write the equation of a line in slope-intercept form.Y = mx + bY = -5x - 1Lets do a couple more to make sure you are expert at this.GUIDED PRACTIEWrite an equation of the line that has the given slope and y-intercept.1. m = 3, b = 1y = x + 13ANSWER 2. m = 2 , b = 4 y = 2x 4ANSWER 3. m = , b =3472y = x +3472ANSWER 51) m = 3, b = -14
2) m = -, b = 4
3) m = -3, b = -7
4) m = 1/2 , b = 0
m = 2, b = 4
m = 0, b = -3Given the slope and y-intercept, write the equation of a line in slope-intercept form.y = 3x - 14y =-x + 4y =-3x - 7y = xy =2x + 4y = - 3
Write an equation of the line shown in slope-intercept form.
b = (0,-2)y = x - 273) The slope of this line is 3/2?True
5) Which is the slope of the line through (-2, 3) and (4, -5)?
-4/3-3/44/3-1/38) Which is the equation of a line whose slope is undefined?x = -5y = 7x = yx + y = 0
Using point-slope form, write the equation of a line that passes through (4, 1) with slope -2.y y1 = m(x x1) y 1 = -2(x 4)Substitute 4 for x1, 1 for y1 and -2 for m.
Write in slope-intercept form.y 1 = -2x + 8 Add 1 to both sidesy = -2x + 9 Using point-slope form, write the equation of a line that passes through (-1, 3) with slope 7.y y1 = m(x x1)y 3 = 7[x (-1)]y 3 = 7(x + 1)
Write in slope-intercept formy 3 = 7x + 7y = 7x + 10Write the equation of a line in slope-intercept form that passes through points (3, -4) and (-1, 4).y2 y1m =x2 x14--4 = -1-3 8 4== 2y2 y1 = m(x x1)Use point-slope form.y + 4 = 2(x 3)Substitute for m, x1, and y1.y + 4 = 2x + 6Distributive propertyWrite in slope-intercept form.y = 2x + 2(-1, -6) and (2, 6)
(0, 5) and (3, 1)
(3, 5) and (6, 6)
(0, -7) and (4, 25)
(-1, 1) and (3, -3)Write the equation of the line in slope-intercept form that passes through each pair of points.GUIDED PRACTICEfor Examples 2 and 3GUIDED PRACTICE4. Write an equation of the line that passes through (1, 6) and has a slope of 4.y = 4x + 105. Write an equation of the line that passes through (4, 2) and is parallel to the line y = 3x 1.y = 3x 14ANSWER ANSWER 15Write an equation of the line that passes through (5, 2) and (2, 10) in slope intercept formSOLUTIONThe line passes through (x1, y1) = (5,2) and (x2, y2) = (2, 10). Find its slope.y2 y1m =x2 x110 (2) = 2 5 12 3== 4y2 y1 = m(x x1)Use point-slope form.y 10 = 4(x 2)Substitute for m, x1, and y1.y 10 = 4x + 8Distributive propertyWrite in slope-intercept form.y = 4x + 1816Which of the following equations passes through the points (2, 1) and (5, -2)?
y = 3/7x + 5b. y = -x + 3c.y = -x + 2d. y = -1/3x + 3y = -3x 3y = -3x + 17y = -3x + 11y = -3x + 59) Which is the equation of a line that passes through (2, 5) and has slope -3?EXAMPLE 3Write an equation in slope-intercept that is perpendicular to y = -4x + 2 and goes through the point (-2, 3)y y1 = m2(x x1)Use point-slope form.y 3 = (x (2))14Substitute for m2, x1, and y1.y 3 = (x +2)14Simplify.y 3 = x +1412Distributive propertyWrite in slope-intercept form.Write equations of parallel or perpendicular lines
19y = 3 (or any number)Lines that are horizontal have a slope of zero. They have run but no rise. The rise/run formula for slope always equals zero since rise = o.y = mx + by = 0x + 3y = 3This equation also describes what is happening to the y-coordinates on the line. In this case, they are always 3.Horizontal Linesx = -2Lines that are vertical have no slope (it does not exist).They have rise, but no run. The rise/run formula for slope always has a zero denominator and is undefined.These lines are described by what is happening to their x-coordinates. In this example, the x-coordinates are always equal to -2.Vertical Lines8) Which is the equation of a line whose slope is undefined?x = -5y = 7x = yx + y = 0
Which of these equations represents a line parallel to the line 2x + y = 6?
Y = 2x + 3Y 2x = 42x y = 8Y = -2x + 1Get Graph paper.Plot this data and discover a line of best fit.The data shows a relationship between the number of years of college and salary earned. Plot this data and create a line of best fit. Remember to pick to two points and create a line in slope-intercept form.
(Scale for x: 0 to 8, Scale for y: 0 to 50 (Go by 5s))Years of college32462.57.5715.54Salary (in $1000)15202247191832103028Step 2: Select two pointsI selected the points (2.5, 19) and (7, 32) on that line to determine the equation of the line.
Which ones did you pick?
Step 3: Find the slope using the two points
Step 4: Use point-slope form to make an equation.
Did you get a similar slope or y-intercept?Prediction Equation (line of best fit) Prediction equation isy = 2.9x + 11.7For example, we can predict that with five years of college education, their salary might be $26,200.
What will 8 years of college get her salary to be?About $33,900Ex. 2: The table below shows the heights and the corresponding ideal weights of adult women. Find a prediction equation for this relationship.
Step 1: Graph the data points.Height (inches)60626466687072Weight (pounds)105111123130139149158Draw a line that appears to be most representative of the data. Thats your line of best fit.Step 2: Choose two points (62, 111) and (66, 130) from the line to find the slope.
Step 3: Now use the slope and one of the points in the slope-intercept form to find the value of b.
Slope-intercept formSubstitute values into form.Multiply 4.8 by 62 to simplify.Subtract 297.6 from both sides.Prediction equation Ex. 3: Draw a scatterplot and a prediction equations to show how typing speed and experience are related. Predict the typing speed of a student who has 11 weeks of experience.Step 1: Graph the data points.Experience (weeks)4781635296710Typing Speed (wpm)334546204030382252444255Scale x: 0 to 10Scale y: 0 to 60 (Go by 5s)Step 2: Choose two points (5, 36) and (8, 49) from the line to find the slope.
Step 3: Now use the point-slope and one of the points to make the equation.
Now plug in 11 for x so that we can predict the speed of typing after 11 weeks.
So there speed is 61.8 words per minute