The sum of twice a number and 6 is equal to the sum of the number and 3
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Answer:
Step-by-step explanation:
<u>Perpendicular lines</u>
Perpendicular lines have slopes whose product is -1. In other words, to find a line that is perpendicular to a given line, the new line must have a that is the opposite reciprocal of the original line.
<u>Passing through a point</u>
Additionally, if a line contains a point, then the point must be a solution to the equation (meaning, when you plug in the "x" and "y", the equation must be true).
<u>Finding our perpendicular line</u>
<u>Work on slope first</u>
To find the slope of the original line, rewrite the original line in slope-intercept form:
In this form, the slope is the number multiplied to the "x", so the original slope is -3/1.
Thus, the slope of the new perpendicular line will be the opposite reciprocal of -3/1 ... which is 1/3.
Writing what we do know about the new perpendicular line, we have
<u>Making sure it passes through the point</u>
This new line is also supposed to contain the point (-3,-1), so (-3,-1) must be a solution to the equation, for whatever constant-value the "b" is. To find out the "b", substitute the known quantities, and solve:
Substituting this into our equation:
<u>Conclusion</u>
So, the equation for a line that is perpendicular to the original line , and that also passes through (-3,-1) is