transform the linear equation -2y=14-6x to slope- intercept form
y=
y=3x-7
To transform the linear equation -2y = 14 - 6x to slope-intercept form (y = mx + b), you need to isolate the y variable.
Step 1: Distribute the (-2) to both terms on the right side of the equation:
-2y = 14 - 6x
Step 2: Simplify the right side of the equation:
-2y = -6x + 14
Step 3: Divide both sides of the equation by -2 to solve for y:
y = (-6x + 14) / (-2)
Step 4: Simplify further:
y = 3x - 7
So, the linear equation -2y = 14 - 6x can be transformed into slope-intercept form as y = 3x - 7.
To transform the linear equation -2y = 14 - 6x into slope-intercept form (y = mx + b), where m represents the slope and b represents the y-intercept, follow these steps:
Step 1: Move the x term to the other side of the equation.
Start with the equation: -2y = 14 - 6x.
To move the variable term (-6x) to the other side of the equation, we need to add 6x to both sides. This will give:
-2y + 6x = 14.
Step 2: Rearrange the terms.
To put the equation in a more standard form, let's rearrange the terms in ascending order of x:
6x - 2y = 14.
Step 3: Divide the entire equation by the coefficient of y.
To isolate y and get it alone on one side, we need to divide the entire equation by the coefficient of y (-2). This will give:
(6x - 2y)/(-2) = 14/(-2).
Simplifying the equation, we have:
-3x + y = -7.
Step 4: Switch the positions of x and y.
In the slope-intercept form, y (the dependent variable) is typically on the left side, while x (the independent variable) is on the right side. So, let's rearrange the equation as:
y - 3x = -7.
Step 5: Finalize the equation.
The equation is now in slope-intercept form (y = mx + b), with the slope (m) being -3 and the y-intercept (b) being -7. Hence, the final form of the equation is:
y = -3x - 7.