find the slope -intercept form for 2x+6y=11
2x+6y = 11
6y = -2x + 11
y = -1/3 x + 11/6
To find the slope-intercept form of the equation 2x + 6y = 11, follow these steps:
Step 1: Write down the given equation: 2x + 6y = 11.
Step 2: Solve the equation for y to isolate it on one side of the equation.
Subtract 2x from both sides:
6y = -2x + 11.
Step 3: Divide every term by 6 to get y by itself.
Divide both sides by 6:
y = (-2/6)x + (11/6).
Step 4: Simplify the fraction.
The fraction -2/6 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 2.
Simplifying -2/6 gives -1/3.
Substitute -1/3 for -2/6:
y = (-1/3)x + (11/6).
Step 5: The equation is now in the slope-intercept form, which is y = mx + b.
The slope (m) can be found by looking at the coefficient of x, which is -1/3.
The y-intercept (b) is the constant term, which is 11/6.
Therefore, the slope-intercept form of the given equation 2x + 6y = 11 is y = (-1/3)x + 11/6.