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Answer :
We are given the equation
[tex]$$12x - 6y = 42.$$[/tex]
To find the slope, we need to rewrite the equation in the slope-intercept form, which is
[tex]$$y = mx + b,$$[/tex]
where [tex]$m$[/tex] is the slope.
Step 1: Isolate the [tex]$y$[/tex]-term
Subtract [tex]$12x$[/tex] from both sides to move the [tex]$x$[/tex]-term to the right-hand side:
[tex]$$12x - 6y - 12x = 42 - 12x,$$[/tex]
which simplifies to
[tex]$$-6y = 42 - 12x.$$[/tex]
Step 2: Solve for [tex]$y$[/tex] by dividing both sides by [tex]$-6$[/tex]
Divide every term by [tex]$-6$[/tex]:
[tex]$$y = \frac{42 - 12x}{-6}.$$[/tex]
Step 3: Simplify the equation
Separate the fraction into two parts:
[tex]$$y = \frac{42}{-6} + \frac{-12x}{-6}.$$[/tex]
Simplify each term:
- [tex]$$\frac{42}{-6} = -7,$$[/tex]
- [tex]$$\frac{-12x}{-6} = 2x.$$[/tex]
Thus, the equation becomes
[tex]$$y = 2x - 7.$$[/tex]
In the slope-intercept form [tex]$y = mx + b$[/tex], the coefficient of [tex]$x$[/tex] is the slope. Therefore, the slope [tex]$m$[/tex] is
[tex]$$m = 2.$$[/tex]
[tex]$$12x - 6y = 42.$$[/tex]
To find the slope, we need to rewrite the equation in the slope-intercept form, which is
[tex]$$y = mx + b,$$[/tex]
where [tex]$m$[/tex] is the slope.
Step 1: Isolate the [tex]$y$[/tex]-term
Subtract [tex]$12x$[/tex] from both sides to move the [tex]$x$[/tex]-term to the right-hand side:
[tex]$$12x - 6y - 12x = 42 - 12x,$$[/tex]
which simplifies to
[tex]$$-6y = 42 - 12x.$$[/tex]
Step 2: Solve for [tex]$y$[/tex] by dividing both sides by [tex]$-6$[/tex]
Divide every term by [tex]$-6$[/tex]:
[tex]$$y = \frac{42 - 12x}{-6}.$$[/tex]
Step 3: Simplify the equation
Separate the fraction into two parts:
[tex]$$y = \frac{42}{-6} + \frac{-12x}{-6}.$$[/tex]
Simplify each term:
- [tex]$$\frac{42}{-6} = -7,$$[/tex]
- [tex]$$\frac{-12x}{-6} = 2x.$$[/tex]
Thus, the equation becomes
[tex]$$y = 2x - 7.$$[/tex]
In the slope-intercept form [tex]$y = mx + b$[/tex], the coefficient of [tex]$x$[/tex] is the slope. Therefore, the slope [tex]$m$[/tex] is
[tex]$$m = 2.$$[/tex]
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