Wednesday, April 10, 2024

Determine the Equation of a Line that Passes through a Given Point and is Parallel to another Line Described by another Equation

 Write an equation passing through a given point (-2,-2) parallel to the line given by the equation: y=-1/5 x+9 Solution

To find the equation of a line parallel to a given line, we first need to identify the slope of the given line. The equation of the given line is:


The slope of this line is 15. Since parallel lines have the same slope, the slope of the line we are trying to find will also be 15.

Next, we use the point-slope form of a line to find the equation of our line. The point-slope form is:


where (1,1) is a point on the line and is the slope. Plugging in the given point (2,2) and the slope 15, we get:

(2)=15((2)) +2=15(+2) +2=1525

Finally, we can rearrange this equation to get it in the standard form:

=15252 =15125

So, the equation of the line passing through the point (2,2) and parallel to the line =15+9 is:


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