Write an equation of a line by using the slope and a point on the line.
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Transcript of Write an equation of a line by using the slope and a point on the line.
![Page 1: Write an equation of a line by using the slope and a point on the line.](https://reader036.fdocuments.us/reader036/viewer/2022082414/56649f1f5503460f94c36e08/html5/thumbnails/1.jpg)
2-4 MORE ABOUT LINEAR EQUATIONS
Write an equation of a line by using the slope and a point on the line.
![Page 2: Write an equation of a line by using the slope and a point on the line.](https://reader036.fdocuments.us/reader036/viewer/2022082414/56649f1f5503460f94c36e08/html5/thumbnails/2.jpg)
Point-Slope Form
Uses one point, (x1, y1) on a line to create an equation
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Writing an Equation
A line passes through (-3, 6) and has a slope of -5.
= m() Plug in the slope an d point = -5() y – 6 = -5(x + 3)
![Page 4: Write an equation of a line by using the slope and a point on the line.](https://reader036.fdocuments.us/reader036/viewer/2022082414/56649f1f5503460f94c36e08/html5/thumbnails/4.jpg)
Graphing
y – 1 = (x – 2) We know the slope is And it passes through the point (2, 1)
![Page 5: Write an equation of a line by using the slope and a point on the line.](https://reader036.fdocuments.us/reader036/viewer/2022082414/56649f1f5503460f94c36e08/html5/thumbnails/5.jpg)
Standard Form of a Linear Equation So far we have learned how to write
linear equations in slope-intercept form and point-slope form.
Standard form is written Ax + By = C where A, B, and C are real numbers
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Intercepts
The x-intercept is the x-coordinate of a point where a graph crosses the x-axis.Found where the y-value is 0
Find x and y intercepts of the graph of 3x + 4y = 24
Sub 0 for y to find x-interceptX =8
Sub 0 for x to find y-interceptY = 6
![Page 7: Write an equation of a line by using the slope and a point on the line.](https://reader036.fdocuments.us/reader036/viewer/2022082414/56649f1f5503460f94c36e08/html5/thumbnails/7.jpg)
Graphing Using Intercepts What is the graph of x – 2y = -2? Find intercepts
X = -2Y = 1
Write as ordered pairs(-2, 0)(0, 1)
Plot the ordered pairs
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Horizontal and Vertical Lines x = 3 Write in standard form: 1x + 0y = 3
y = 3 Standard form: 0x + 1y = 3
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Transforming to Standard Form
What is y = in standard form Get rid of fractions by multiplying by 7 7y = 7() Distribute: 7y = -3x + 35 Add 3x: 7y + 3x = 35 Done! These equations, though they look
different, are equivalent.
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Parallel Lines
Lines in the same plane that never intersect.
Nonvertical lines are parallel if they have the same slope and different y-intercepts.
Vertical lines are parallel if they have different x-intercepts.
Ex: Same slope, different y-intercept
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Perpendicular lines Lines that intersect to form right angles
Two nonvertical lines are perpendicular if the product of their slopes is -1.The slope is the opposite reciprocal.Ex: the opposite reciprocal of is since their
product is -1. A vertical line and a horizontal line are
always perpendicular.