Put the following equation of a line into slope-intercept form, simplifying all fractions.
6x+4y=8
To put the equation 6x + 4y = 8 into slope-intercept form, we need to solve for y.
First, let's subtract 6x from both sides:
4y = -6x + 8
To isolate y, divide both sides of the equation by 4:
y = (-6/4)x + 8/4
Simplifying the fractions gives us:
y = (-3/2)x + 2
To put the equation of a line into slope-intercept form, which is in the form of y = mx + b, you need to isolate the y variable on one side of the equation. Follow these steps to simplify the equation 6x + 4y = 8 and rewrite it in slope-intercept form:
1. Begin with the equation: 6x + 4y = 8.
2. To isolate the y variable, you need to get rid of the 6x term. Subtract 6x from both sides of the equation:
6x - 6x + 4y = -6x + 8
As a result, the equation simplifies to: 4y = -6x + 8.
3. To further simplify the equation, divide every term by 4 to isolate the y variable:
(4y)/4 = (-6x + 8)/4
Thus, the equation becomes: y = (-6/4)x + 8/4.
4. Simplify the fractions:
y = (-3/2)x + 2.
Now, the equation 6x + 4y = 8 is in slope-intercept form, y = mx + b, with the slope (m) being -3/2 and the y-intercept (b) being 2.
To put the equation of a line into slope-intercept form (y = mx + b), where m represents the slope and b represents the y-intercept, we need to isolate the y variable on one side of the equation.
Let's simplify the given equation step by step:
1. Start with the original equation:
6x + 4y = 8
2. To isolate the y term, we need to get rid of the 6x term. To do this, we subtract 6x from both sides of the equation:
4y = -6x + 8
3. Next, we want to get y alone on one side of the equation. We can do this by dividing both sides of the equation by 4:
(4y)/4 = (-6x + 8)/4
Simplifying further:
y = (-6/4)x + 2
4. Finally, we can simplify the fraction -6/4 by dividing both the numerator and denominator by their greatest common divisor (GCD), which is 2:
y = (-3/2)x + 2
Hence, the equation 6x + 4y = 8 in slope-intercept form is y = (-3/2)x + 2.