An engineer studying fuel usage collected data on the speed a car traveled (in kilometers per hour) and how much fuel it used (i
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is the equation of the line that is perpendicular to this line and passes through the point (6, -2)
y = 7x - 44 equation of the line that is parallel to this line and passes through the point (6, -2)
<em><u>Solution:</u></em>
<em><u>Given that line is:</u></em>
y = 7x - 9
<em><u>The equation of line in slope intercept form is given as:</u></em>
y = mx + b ------ eqn 1
Where, "m" is the slope of line and "b" is the y intercept
On comparing eqn 1 with y = 7x - 9 we get,
m = 7
<h3><u>Find the equation of the line that is perpendicular to this line and passes through the point (6, -2)</u></h3>We know that,
Product of slope of a line and slope of line perpendicular to given is always -1
Therefore,
Now find the equation of line:
Thus the equation of line perpendicular to given line is found
<h3><u>Find the equation of the line that is parallel to this line and passes through the point (6, -2)</u></h3>Slopes of parallel lines are equal
Therefore, m = 7
<em><u>Substitute m = 7 and (x, y) = (6, -2) in eqn 1</u></em>
-2 = 7(6) + b
-2 = 42 + b
b = -44
<em><u>Substitute m = 7 and b = -44 in eqn 1</u></em>
y = 7x - 44
Thus equation of line parallel to given line is found