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Question

Question: How do you write \(3x = - 2y + 4\) in slope-intercept form?...

How do you write 3x=2y+43x = - 2y + 4 in slope-intercept form?

Explanation

Solution

First of all this is a very simple and a very easy problem. The general equation of a slope-intercept form of a straight line is y=mx+cy = mx + c, where mm is the gradient and y=cy = c is the value where the line cuts the y-axis. The number cc is called the intercept on the y-axis. Based on this provided information we try to find the equation of the straight line.

Complete step-by-step answer:
We are given that an equation of a line is given by
We know that the equation of the straight line is given by: 3x=2y+43x = - 2y + 4.
Now consider the given equation, as shown below:
3x=2y+4\Rightarrow 3x = - 2y + 4
Here the slope of the equation is obtained when expressed the given equation in slope-intercept form as given below:
Rearrange the equation such that the yy term is on the left hand side of the equation, whereas the xx term and the constant is on the right hand side of the equation, as given below:
2y=3x+4\Rightarrow 2y = - 3x + 4
Now divide the above equation by 2, so as to remove the coefficient of the yy term on the left hand side of the equation, as given below:
y=32x+2\Rightarrow y = \dfrac{{ - 3}}{2}x + 2
Here the above equation is expressed in the form of the slope intercept form which is y=mx+cy = mx + c.
The slope- intercept form of 3x=2y+43x = - 2y + 4 is y=32x+2y = \dfrac{{ - 3}}{2}x + 2

Final Answer: The slope intercept form of 3x=2y+43x = - 2y + 4 is equal to y=32x+2y = \dfrac{{ - 3}}{2}x + 2.

Note:
Please note that while solving such kind of problems, we should understand that if the y-intercept value is zero, then the straight line is passing through the origin, which is in the equation of y=mx+cy = mx + c, if c=0c = 0, then the equation becomes y=mxy = mx, and this line passes through the origin, whether the slope is positive or negative.