PLEASE HELP Both of the lines slope is equal to -7/4 but how do I know if they’re parallel ?
1 answer:
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The sum of the inner angles of any triangle is always 180°, i.e. you have
In the particular case of an equilater triangle, all three angles are the same, so
and the expression becomes
which implies
So, if you rotate the triangle with respect to its center by 60 degrees, the triangle will map into itself. In particular, if you want point A to be mapped into point B, you have to perform a counter clockwise rotation of 60 degrees with respect to the center of the triangle.
Of course, this is equivalent to a clockwise rotation of 120 degrees.
Finally, both solutions admit periodicity: a rotation of 60+k360 degrees has the same effect of a rotation of 60 degrees, and the same goes for the 120 one (actually, this is obvisly true for any rotation!)
Answer:
1a. y-intercept: 12
1b. slope: -3/2
1c. equation: y = -3/2x +12
2a. y-intercept: -9
2b. slope: 2
2c. equation: y = 2x -9
Step-by-step explanation:
<h3>1.</h3>A) We observe the pattern to be <em>x-values in the table increase by 2, while y-values in the table decrease by 3</em>. We notice the first x-value is 2, so extending the table upward to x=0 would tell us the y-intercept. That is, adding 3 to the first y-value will give the y-intercept as (x, y) = (0, 12).
B) We have already observed that the "rise" (change in y) is -3 for each "run" (change in x) of 2. The slope is the ratio of these changes:
slope = m = rise/run = -3/2
C) From the above, we know that m=-3/2 and b=12. Putting these values into the equation for the line gives ...
y = -3/2x +12
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<h3>2.</h3>A) We observe the pattern to be <em>y-values increase by 2 while x-values increase by 1</em>. As before, we can find the point that would go before the first one shown in the table. It will have an x-value of 0 and a y-value of -9.
the y-intercept is -9
the slope is 2/1 = 2
the equation is y = 2x -9
