Respuesta :
Hello!
Slope-intercept form is this one: [tex]y=a*x+b[/tex] where a is the slope and b the intercept.
So, for transforming these equations to Slope-Intercept you'll need to rearrange the equations by adding or subtracting the same amounts on both sides of the equation (as a rule of thumb, sums are transformed into subtractions and multiplications into divisions).
1) 3x + y = 12
You should notice that Y and X are on the same side of the equation, so by subtracting 3x on both sides of the equation you'll cancel X on the left side:
[tex]3x+y-3x=12-3x \\ y=12-3x[/tex]
To finish, we rearrange this equation to the form y=a*x+b
[tex]y=-3x+12[/tex]
So, the slope is -3 and the intercept is 12
2) 8=y+5x
You should notice that Y and X are on the same side of the equation, so by subtracting 5x on both sides of the equation you'll cancel X on the right side:
[tex]8-5x=y+5x-5x \\ 8-5x=y[/tex]
To finish, we rearrange this equation to the form y=a*x+b
[tex]y=-5x+8[/tex]
So, the slope is -5 and the intercept is 8
3) 6x + 3y = -9
You should notice that Y and X are on the same side of the equation, so by subtracting 6x on both sides of the equation you'll cancel X on the left side:
[tex]6x+3y-6x=-9-6x \\ 3y=-9-6x[/tex]
Now, you should notice that y has a number that is multiplying it, so you'll need to divide the entire equation by 3 to cancel this number on the left side.
[tex] \frac{3}{3}y= \frac{9}{3}- \frac{6}{3}x \\ y=3-2x [/tex]
To finish, we rearrange this equation to the form y=a*x+b
[tex]y=-2x+3[/tex]
So, the slope is -2 and the intercept is 3
4) x - 5y = 55
You should notice that Y and X are on the same side of the equation, so by subtracting x on both sides of the equation you'll cancel X on the left side:
[tex]x-5y-x=-55-x \\ -5y=-55-x[/tex]
Now, you should notice that y has a number that is multiplying it, so you'll need to divide the entire equation by -5 to cancel this number on the left side.
[tex]\frac{-5}{-5}y= \frac{55}{-5}- \frac{1}{-5}x \\ y=-11+ \frac{1}{5}x[/tex]
To finish, we rearrange this equation to the form y=a*x+b
[tex]y=\frac{1}{5}x-11[/tex]
So, the slope is 1/5 and the intercept is -11
5) -4x-y=-2
You should notice that Y and X are on the same side of the equation, so by adding 4x on both sides of the equation you'll cancel X on the left side:
[tex]-4x-y+4x=-2+4x \\ -y=2+4x[/tex]
Now, you should notice that y has a number that is multiplying it, so you'll need to divide the entire equation by -1 to cancel this number on the left side.
[tex] \frac{-1}{-1} y= \frac{-2}{-1}+ \frac{4}{-1}x \\ y=2-4x[/tex]
To finish, we rearrange this equation to the form y=a*x+b
[tex]y=-4x+2[/tex]
So, the slope is -4 and the intercept is 2
6) -16 = -4x + 2y
You should notice that Y and X are on the same side of the equation, so by adding 4x on both sides of the equation you'll cancel X on the right side:
[tex]-16+4x=-4x+2y+4x \\ -16+4x=2y[/tex]
Now, you should notice that y has a number that is multiplying it, so you'll need to divide the entire equation by 2 to cancel this number on the right side.
[tex] \frac{-16}{2}+ \frac{4}{2} x= \frac{2}{2}y \\ -8+2x=y [/tex]
To finish, we rearrange this equation to the form y=a*x+b
[tex]y=2x-8[/tex]
So, the slope is 2 and the intercept is -8
I hope that this helps. Have a nice day!
Slope-intercept form is this one: [tex]y=a*x+b[/tex] where a is the slope and b the intercept.
So, for transforming these equations to Slope-Intercept you'll need to rearrange the equations by adding or subtracting the same amounts on both sides of the equation (as a rule of thumb, sums are transformed into subtractions and multiplications into divisions).
1) 3x + y = 12
You should notice that Y and X are on the same side of the equation, so by subtracting 3x on both sides of the equation you'll cancel X on the left side:
[tex]3x+y-3x=12-3x \\ y=12-3x[/tex]
To finish, we rearrange this equation to the form y=a*x+b
[tex]y=-3x+12[/tex]
So, the slope is -3 and the intercept is 12
2) 8=y+5x
You should notice that Y and X are on the same side of the equation, so by subtracting 5x on both sides of the equation you'll cancel X on the right side:
[tex]8-5x=y+5x-5x \\ 8-5x=y[/tex]
To finish, we rearrange this equation to the form y=a*x+b
[tex]y=-5x+8[/tex]
So, the slope is -5 and the intercept is 8
3) 6x + 3y = -9
You should notice that Y and X are on the same side of the equation, so by subtracting 6x on both sides of the equation you'll cancel X on the left side:
[tex]6x+3y-6x=-9-6x \\ 3y=-9-6x[/tex]
Now, you should notice that y has a number that is multiplying it, so you'll need to divide the entire equation by 3 to cancel this number on the left side.
[tex] \frac{3}{3}y= \frac{9}{3}- \frac{6}{3}x \\ y=3-2x [/tex]
To finish, we rearrange this equation to the form y=a*x+b
[tex]y=-2x+3[/tex]
So, the slope is -2 and the intercept is 3
4) x - 5y = 55
You should notice that Y and X are on the same side of the equation, so by subtracting x on both sides of the equation you'll cancel X on the left side:
[tex]x-5y-x=-55-x \\ -5y=-55-x[/tex]
Now, you should notice that y has a number that is multiplying it, so you'll need to divide the entire equation by -5 to cancel this number on the left side.
[tex]\frac{-5}{-5}y= \frac{55}{-5}- \frac{1}{-5}x \\ y=-11+ \frac{1}{5}x[/tex]
To finish, we rearrange this equation to the form y=a*x+b
[tex]y=\frac{1}{5}x-11[/tex]
So, the slope is 1/5 and the intercept is -11
5) -4x-y=-2
You should notice that Y and X are on the same side of the equation, so by adding 4x on both sides of the equation you'll cancel X on the left side:
[tex]-4x-y+4x=-2+4x \\ -y=2+4x[/tex]
Now, you should notice that y has a number that is multiplying it, so you'll need to divide the entire equation by -1 to cancel this number on the left side.
[tex] \frac{-1}{-1} y= \frac{-2}{-1}+ \frac{4}{-1}x \\ y=2-4x[/tex]
To finish, we rearrange this equation to the form y=a*x+b
[tex]y=-4x+2[/tex]
So, the slope is -4 and the intercept is 2
6) -16 = -4x + 2y
You should notice that Y and X are on the same side of the equation, so by adding 4x on both sides of the equation you'll cancel X on the right side:
[tex]-16+4x=-4x+2y+4x \\ -16+4x=2y[/tex]
Now, you should notice that y has a number that is multiplying it, so you'll need to divide the entire equation by 2 to cancel this number on the right side.
[tex] \frac{-16}{2}+ \frac{4}{2} x= \frac{2}{2}y \\ -8+2x=y [/tex]
To finish, we rearrange this equation to the form y=a*x+b
[tex]y=2x-8[/tex]
So, the slope is 2 and the intercept is -8
I hope that this helps. Have a nice day!
