Question
Question: How do you write \(3x = - 2y + 4\) in slope-intercept form?...
How do you write 3x=−2y+4 in slope-intercept form?
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+c, where m is the gradient and y=c is the value where the line cuts the y-axis. The number c 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+4.
Now consider the given equation, as shown below:
⇒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 y term is on the left hand side of the equation, whereas the x term and the constant is on the right hand side of the equation, as given below:
⇒2y=−3x+4
Now divide the above equation by 2, so as to remove the coefficient of the y term on the left hand side of the equation, as given below:
⇒y=2−3x+2
Here the above equation is expressed in the form of the slope intercept form which is y=mx+c.
The slope- intercept form of 3x=−2y+4 is y=2−3x+2
Final Answer: The slope intercept form of 3x=−2y+4 is equal to y=2−3x+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+c, if c=0, then the equation becomes y=mx, and this line passes through the origin, whether the slope is positive or negative.