Select the correct answer.
Given the formula below, solve for [tex]$x$[/tex].
[tex]$y-y_1=m\left(x-x_1\right)$[/tex]
A. [tex]$x=\frac{y-y_1+x_1}{m}$[/tex]
B. [tex]$x=\frac{y-y_1}{m}+x_1$[/tex]
C. [tex]$x=\frac{m\left(y-y_1\right)}{x_1}$[/tex]
D. [tex]$x=\frac{y-y_1}{m}-x_1[/tex]
Answer (2)
Divide both sides of the equation by m : m y − y 1 = x − x 1 .
Add x 1 to both sides: m y − y 1 + x 1 = x .
Isolate x : x = m y − y 1 + x 1 .
The correct answer is: x = m y − y 1 + x 1 .
Explanation
Understanding the Problem We are given the equation y − y 1 = m ( x − x 1 ) and asked to solve for x . This involves isolating x on one side of the equation using algebraic manipulations.
Dividing by m First, we divide both sides of the equation by m to get rid of the multiplication by m on the right side:
Result of Division m y − y 1 = x − x 1
Adding x_1 Next, we add x 1 to both sides of the equation to isolate x :
Isolating x m y − y 1 + x 1 = x
Final Solution Thus, we have solved for x and found that:
Solution for x x = m y − y 1 + x 1
Selecting the Correct Option Comparing our solution to the given options, we see that it matches option B.
Examples
The formula y − y 1 = m ( x − x 1 ) is known as the point-slope form of a linear equation. It's useful in many real-world scenarios, such as determining the equation of a line when you know a point on the line ( x 1 , y 1 ) and the slope m . For example, if you are tracking the altitude of a plane climbing at a constant rate, you can use this formula to predict its altitude at any given time. If the plane is at an altitude of 1000 feet at time 0 and climbs at a rate of 500 feet per minute, you can determine its altitude at any time x minutes using this formula.
To solve for x in the equation y − y 1 = m ( x − x 1 ) , we isolate x by first dividing by m and then adding x 1 . The correct answer is option B: x = m y − y 1 + x 1 .
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