The equation of the line that is parallel to the line whose equation is 3x-2y=7 would be y = 3/2x + b, in which b can be any real number.
How are parallel straight lines related?
Parallel lines have the same slope since the slope is like a measure of steepness and since parallel lines are of the same steepness, thus, are of the same slope.
We have been given a parallel line with has equation
3x-2y=7
In order to solve this, the slope of the original line.
3x - 2y = 7
-2y = -3x + 7
y = 3/2x - 7/2
thus its slope is 3/2.
thus, the slope of the needed line is 3/2 too.
we know that any line that is parallel to that would have this slope.
So anything is written in the form:
y = 3/2x + b
The equation of the line that is parallel to the line whose equation is 3x-2y=7 would be y = 3/2x + b, in which b can be any real number.
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Let <em>n</em> be the unknown number. We can write it as
<em>n</em> = 10<em>a</em> + <em>b</em>
with <em>a</em> and <em>b</em> integers between 1 and 9 (either with positive or negative sign).
Reversing the digits gives another number
<em>m</em> = 10<em>b</em> + <em>a</em>
The first number is increased by 54 when the digits are reversed, which means
<em>m</em> = <em>n</em> + 54 → 10<em>b</em> + <em>a</em> = 10<em>a</em> + <em>b</em> + 54 → 9<em>b</em> - 9<em>a</em> = 54 → <em>b</em> - <em>a</em> = 6
The digit in the tens place of <em>n</em> is 3 times the digit in the ones place, so
<em>a</em> = 3<em>b</em>
Substitute this into the previous equation and solve for <em>b</em> :
<em>b</em> - <em>a</em> = <em>b</em> - 3<em>b</em> = -2<em>b</em> = 6 → <em>b</em> = -3
Solve for <em>a</em> :
<em>a</em> = 3<em>b</em> = 3(-3) = -9
Then the original number is <em>n</em> = 10<em>a</em> + <em>b</em> = 10(-9) + (-3) = -93
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Step-by-step explanation:
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