Are these equations equivalent?
2 answers:
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Answer:
○ 3
○ y + ½ = 3(x - 2)
○ Multiply both sides of the equation by 3. The Standard Form of the equation is 12x - 2y = 24.
○ 5x - 3y = 15
○ y = ½x + 5⁄2
Step-by-step explanation:
Find the <em>rate</em><em> </em><em>of</em><em> </em><em>change</em><em> </em>[<em>slope</em>]:
-y₁ + y₂\-x₁ + x₂ = m → (-1, 1) and (-2, -2)
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According to the Point-Slope Formula, <em>y - y₁ = m(x - x₁)</em>, all the negative symbols give the OPPOSITE terms of what they really are, so be EXTREMELY CAREFUL inserting this coordinate into the formula with their CORRECT SIGNS:
(2, -½) → y + ½ = 3(x - 2)
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We do not want fractions in our Standard Equation, so multiply by the denominator to get rid of it:
-3[4x - ⅔y = 8] → -12x + 2y = -24
** They should have multiplied by -3 instead of 3 because that negative is hooked up to everything in the fraction, but since the exercise gave you 12x - 2y = 24, go with 12x - 2y = 24.
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If you would take a look at this graph real closely, you will see that this graph intersects the y-axis and x-axis at ENDPOINTS, so to find the x-intercept, you simply plug in <em>zero</em> for <em>y</em>: 5x = 15, and you will know right away that <em>x</em><em> </em>is set to equal 3, which is what you see in the graph, (3, 0). Now, to find the y-intercept, you simply plug in <em>zero</em><em> </em>for <em>x</em>: -3y = 15, and you will know right away that <em>y</em><em> </em>is set to equal -5, which is what you see on the graph as well, (0, -5). With that being said, you have your answer.
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y - 3 = ½(x - 1)
y - 3 = ½x - ½
+ 3 + 3
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y = ½x + 2½
* 2½ = 5⁄2
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Answer:
(A) At the intersection of the first line with the third line, the bottom left angle is 115 degrees. At the intersection of the second line with the third line, the uppercase left angle is 65 degrees.
Step-by-step explanation:
Alternate interior angles are supplementary when parallel lines are crossed by a transversal. The first description seems to be describing alternate interior angles. (See attachment)
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<em>Comment on orientation</em>
If the transversal is oriented horizontally, then the descriptions of the angles will be of different angles than assumed here.
