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Writing equations of lines











































Linear Equation

Write the equation of the line with a slope of -1/3 and passing through the
point (6, -4).

Begin with the slope-intercept form or the point-slope form of the equation.

Comments for Writing equations of lines

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Apr 06, 2013
Linear Equation
by: Staff


Answer


Part I


Slope Intercept Form of a Linear Equation

Slope Intercept Form of a Linear Equation



m = slope

b = y-intercept

since the slope is -1/3, then m = -1/3

this line will pass through the following point: (6, -4)

at that point

x = 6

y = -4

The slope-intercept form of a linear equation has
four
unknown variables: y, m, x, and b.

However, when a graph of the linear equation passes

through the point (6, -4), three of these values are known: x (= 6), y (= -4), and m (= -1/3).

The known values for x (= 6), y (= -4), and m (= -1/3) can be substituted for the variables x, y, and m in the linear equation.



When this is done, the equation has only one unknown variable: "b", the y-intercept.

The known values for x (= 6), y (= -4), and m (= -1/3) can be substituted for the variables x, y, and m in the linear equation.






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Apr 06, 2013
Linear Equation
by: Staff

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Part II


Solve for "b", the y-intercept

Multiply (-1/3)*6 on the right side of the equation

Multiply (-1/3)*6 on the right side of the equation.





add 2 to each side of the equation

Add 2 to each side of the equation.





since the values of both "m" and "b" are now known, these values can be substituted for those variables in the standard slope-intercept form of the linear equation:

Since the values of both






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Apr 06, 2013
Linear Equation
by: Staff

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Part III


Final Answer:

Final Answer:  Linear Equation with slope -1/3 passing through point (6, -4).






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check the answer

since the straight line passes through the point (6, -4), when x = 6 the equation should compute -4 for y

Since the straight line passes through the point (6, -4), when x = 6 the equation should compute -4 for y.




A graph of the equation is shown below:

Graph of straight line equation y = (-1/3)x - 2.








Thanks for writing.

Staff
www.solving-math-problems.com


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