Definitions
The Standard Form of the Equation of a Line Ax + By = C where A, B, and C are real
numbers |
The Point-Slope Form of the Equation of a Line The equation of a line with slope m
and passing through y - y _{1}
= m ( x - x_{1}
) where m is the slope and ( x_{1}, y _{1})
is the point given |
The Slope-Intercept Form of the Equation of a Line The equation of a line with slope m
and y = mx + b where m is the slope and ( 0, b ) is
the y-intercept |
Example Problem 1
Find the equation of the line that
passes through the points ( -3, 4 ) and ( 1, 7 ). |
Solution 1
The first step is to determine the slope
of the line. In order to determine the slope of the line,
we must use the formula m = ( y_{2} - y_{1} ) / ( x_{2} - x_{1} ). This gives us,
Therefore, the slope of the line is equal to 3/4. Now, the next step is to apply the point-slope
formula. To do so, we must choose one of the points, ( x_{1}, y_{1}
), and insert it and the slope into the formula which
will give us,
Finally, now that we have the equation
of the line in
As you can see, when x = 0, y
= 25/4. We now have the equation of the line in
slope-intercept form and the Note: If the question does not specify a specific form for the equation of the line then an equation in either point-slope or slope-intercept form would be a correct answer. |
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