What is the slope and the y-intercept of the equation 3+2x=−15/2y. Write the y-intercept as an ordered pair.
To convert the equation to slope-intercept form, we need to solve for y:
3+2x=−15/2y
Divide both sides by -15/2:
-2/15(3+2x) = y
Simplify:
y = -2/15(3) - 2/15(2x)
y = -2/5 - 4/15x
Therefore, the slope is -4/15 and the y-intercept is (0, -2/5).
4x−8y=24 to slope-intercept form
To convert the equation to slope-intercept form, we need to solve for y:
4x - 8y = 24
First, subtract 4x from both sides:
-8y = -4x + 24
Next, divide both sides by -8:
y = (1/2)x - 3
Now the equation is in slope-intercept form, where the slope is 1/2 and the y-intercept is -3.
To determine the slope and y-intercept of the equation, it needs to be rewritten in slope-intercept form, which has the form y = mx + b, where m represents the slope and b represents the y-intercept.
Starting with the given equation: 3 + 2x = -15/2y
First, let's isolate y by dividing both sides of the equation by (-15/2):
(3 + 2x) / (-15/2) = y
Dividing by a fraction is equivalent to multiplying by its reciprocal:
(3 + 2x) * (-2/15) = y
Multiplying both terms by (-2/15) gives:
(2x + 3) * (-2/15) = y
We can simplify the equation as follows:
(-2/15) * (2x + 3) = y
Expanding the expression inside the parentheses:
(-2/15) * 2x + (-2/15) * 3 = y
Simplifying further:
(-4/15)x + (-6/15) = y
(-4/15)x - 2/5 = y
Finally, we have the equation in slope-intercept form: y = (-4/15)x - 2/5
Now we can identify the slope (m) and y-intercept (b) from this form.
The slope (m) is the coefficient of x, which is -4/15.
The y-intercept (b) is the constant term, which is -2/5.
Writing the y-intercept as an ordered pair: (0, -2/5).