The table represents a linear function. What is the slope of the function?
2 answers:
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Part 1
we have the points (0,6) and (-8,0)
Find out the slope
m=(0-6)/(-8-0)
m=-6/-8
m=3/4
The equation of L1 is
y=(3/4)x+6
Graph the given line
see the figure below
Find out the measure of angle X
tan(X)=6/8 -----> by TOA
X=tan^-1(3/4)
<h2>X=36.87 degrees</h2>Part 2
step1
Find out the equation of the perpendicular line to the Line L1 that passes through the origin
Remember that
If two lines are perpendicular
then
their slopes are negative reci[rocal
so
the slope of the perpendicular line to L1 is
m=-4/3
step 2
Find out the equation of the line
y=-(4/3)x
step 3
Find out the intersection point between L1 and the perpendicular line
we have the system
y=(3/4)x+6 ----------> L1
y=-(4/3)x
Solve by graphing
step 4
Find out the distance between points (-2.88,3.84) and (0,0)
Applying the formula of the distance between two points
therefore
The answer Part 2 is
<h2>The distance is 4.8 units</h2>part 3
<h2>The point in L1 nearest to the origin is the point (-2.88,3.84)</h2>