Write an Equation Given Two Points
Key Questions
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Slope Formula
The slope formula of the line passing through the points
#(x_1,y_1)# and#(x_2,y_2)# can be found by:#m={y_2-y_1}/{x_2-x_1}# So to find the slope of a line segment joining the points ( 2, - 5) and (- 2, 4).
First, label the points as
#x_1# = 2,#y_1# = - 5,#x_2# = -2 and#y_2# = 4#m={y_2-y_1}/{x_2-x_1}# =#{4- -5}/{-2- 2}# =#{9}/{-4}# =#{-9}/{4}# So, the slope (
#m# ) = -9/4. -
No, it does not as long as the point is on the line. You will end up with the same value for the
#y# -intercept.
I hope that this was helpful.
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If the slope of a line is undefined, then the line is a vertical line, so it cannot be written in slope-intercept form, but it can be written in the form:
#x=a# , where#a# is a constant.
Example
If the line has an undefined slope and passes through the point
#(2,3)# , then the equation of the line is#x=2# .
I hope that this was helpful.
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Answer:
Use the differences in the y and x values to find the slope then substitute the values of one point into the equation to find b the y intercept.
Explanation:
Slope =
#( y_1-y_2)/(x_1-x_2)=m# By putting the x and y values for the two points into the slope equation the value for m can be found.
The equation of a line in the slope intercept form is
# y = mx +b # After finding m using the slope equation substitute one set of point values for y and x. This leaves b as the only unknown. Slope the resulting equation for b.
Questions
Forms of Linear Equations
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Write an Equation Given the Slope and a Point
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Write an Equation Given Two Points
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Write a Function in Slope-Intercept Form
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Linear Equations in Point-Slope Form
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Forms of Linear Equations
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Applications Using Linear Models
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Equations of Parallel Lines
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Equations of Perpendicular Lines
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Families of Lines
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Fitting Lines to Data
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Linear Interpolation and Extrapolation
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Problem Solving with Linear Models
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Dimensional Analysis