2 answers:
Answer: 2x + 5y = -5
Step-by-step explanation:
Two lines are said to be parallel if they have the same slope.
The equation of the line given :
2x + 5y = 10
To find the slope , we will write it in the form y = mx + c , where m is the slope and c is the y - intercept.
2x + 5y = 10
5y = -2x + 10
y = -2/5x + 10/5
y = -2/5x + 2
This means that the slope is -2/5 ,the line that is parallel to this line will also have a slope of -2/5.
using the formula:
= m (
) to find the equation of the line , we have
y - 1 = -2/5(x -{-5})
y - 1 = -2/5 ( x + 5 )
5y - 5 = -2 ( x + 5 )
5y - 5 = -2x - 10
5y + 2x = -10 + 5
therefore :
2x + 5y = -5 is the equation of the line that is parallel to 2x + 5y = 10
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Since you haven't provided the graph, I'll explain each one and you choose the one suiting your given.
<u>The parent modulus function is:</u>
g(x) = |x|
It is centered at the origin and opens upwards.
A coefficient inside the modulus |x+k| means that the function is shifted along the x-axis
If "k" is <u>positive</u>, the shift will be to the <u>left</u>. If "k" is <u>negative</u>, the shift will be to the <u>right</u>.
A coefficient outside the modulus |x| + h means that the function is shifted along the y-axis
If "h" is <u>positive</u>, the shift will be <u>upwards</u>. If "h" is <u>negative,</u> the shift will be <u>downwards</u>.
<u>Now, let's check each of the options:</u>
<u>g(x) = |x+4| - 2 :</u>
This function is shifted 4 units to the left and 2 units down. It will be centered at (-4,-2). Check the blue graph in the attachment.
<u>g(x) = |x-4| - 2 :</u>
This function is shifted 4 units to the right and 2 units down. It will be centered at (4,-2). Check the black graph in the attachment.
<u>g(x) = |x-2| - 4 :</u>
This function is shifted 2 units to the right and 4 units down. It will be centered at (2,-4). Check the red graph in the attachment.
<u>g(x) = |x-2| + 4 :</u>
This function is shifted 2 units to the right and 4 units up. It will be centered at (2,4). Check the green graph in the attachment.
All 4 graphs are shown in the attached picture.
Hope this helps :)
