Zack is taking inventory of loaves of bread at the grocery store where he works. There are 20 loaves in a full case, and Zack ha
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Answer:
y=-3x+5
Explanation:
Given a line L such that:
• L has y-intercept (0,5); and
,• L is perpendicular to the line with equation y=(1/3)x+1.
We want to find the equation of the line in the slope-intercept form.
The slope-intercept form of the equation of a straight line is given as:
Comparing the given line with the form above:
Next, we find the slope of the perpendicular line L.
• Two lines are perpendicular if the product of their slopes is -1.
Let the slope of L = m1.
Since L and y=(1/3)x+1 are perpendicular, therefore:
The y-intercept of L is at (0,5), therefore:
Substitute the slope, m=-3, and y-intercept, b=5 into the slope-intercept form.
The equation of line L is:
In counterclockwise order that's
R(2,4), Q(-4,4), U(-4,3), T(2,-3), S(5,-3)
That's a trapezoid, height 7 upper base 6, lower base 9, so average base 15/2 and area 7(15)/2 = 105/2 = 52.5.
Answer: 52.5
The shoelace theorem gives the answer without thinking. We write the list on top of itself shifted and add up the cross produces:
R(2,4), Q(-4,4), U(-4,-3), T(2,-3), S(5,-3)
Q(-4,4), U(-4,-3), T(2,-3), S(5,-3), R(2,4),