Rewrite the given equation in slope intercept form y = mx + b. Use fractions for the slope and the y-intercept, as needed.
4/5x + 6/5y=4
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To rewrite the given equation in slope-intercept form (y = mx + b), we need to isolate y on one side of the equation.
Starting with the equation:
4/5x + 6/5y = 4
We can begin by moving the 4/5x term to the right side of the equation by subtracting 4/5x from both sides:
6/5y = -4/5x + 4
Next, we can simplify the terms on the right side of the equation by finding a common denominator:
6/5y = (-4/5x * 5/5) + (4 * 5/5)
6/5y = (-20/25x) + (20/5)
6/5y = (-20/25x) + (100/25)
Now, combining the terms on the right side of the equation, we have:
6/5y = (-20/25x) + (100/25)
Simplifying further gives:
6/5y = (-20x + 100)/25
To isolate y, we can multiply both sides by the reciprocal of 6/5, which is 5/6:
(5/6)(6/5)y = (5/6)((-20x + 100)/25)
This results in:
y = (-20/30x + 100/30)/25
Simplifying the terms:
y = (-2/3x + 10/3)/25
Lastly, to express the slope and y-intercept as fractions:
y = -2/3x + 10/3
Therefore, the equation in slope-intercept form is y = -2/3x + 10/3.
To rewrite the given equation in slope-intercept form (y = mx + b), we need to isolate y on one side of the equation.
First, let's rearrange the equation:
4/5x + 6/5y = 4
We can start by moving the 4/5x term to the right side of the equation:
6/5y = 4 - 4/5x
To eliminate the fraction in front of y, we can multiply both sides of the equation by the reciprocal of 6/5, which is 5/6:
(5/6)(6/5)y = (5/6)(4 - 4/5x)
Simplifying:
y = (20/6) - (4/6)x
Now, let's simplify the fractions:
y = 10/3 - 2/3x
The equation is now in slope-intercept form (y = mx + b), with the slope (m) being -2/3 and the y-intercept (b) being 10/3.