Find the slope of the line. (If an answer is undefined, enter UNDEFINED.)
−4x + 5y = 9
my answer:
−4x + 5y = 9
5y = 4x+9
y=(4/5)x +(9/5)
my teacher never said about converting fractions to decimals and vice versa. does it matter if I put it y=(4/5)x +(9/5) to fractions?
It is in fractions
you could say:
y = (4x + 9)/5, same thing
or
y = 0.8x + 1.8 , it's all the same
Converting fractions to decimals or vice versa may not always be required, but it can help you simplify the equation and find the slope more easily.
In the given equation, −4x + 5y = 9, we want to find the slope. To do that, let's put the equation in slope-intercept form, which is of the form y = mx + b, where m is the slope.
First, let's isolate the y-term by adding 4x to both sides:
−4x + 4x + 5y = 4x + 9
5y = 4x + 9
Next, divide every term by 5 to solve for y:
(5y)/5 = (4x)/5 + 9/5
y = (4/5)x + (9/5)
So, your answer of y = (4/5)x + (9/5) is correct and is in the form of the equation required to find the slope.
Whether you choose to leave the slope and y-intercept as fractions or convert them to decimals is a matter of personal preference or the specific requirements of your teacher. In some cases, using fractions may be preferred if the numbers are simple and more easily understood.
However, if needed, you can easily convert the fractions to decimals by dividing the numerator by the denominator. In this case, (4/5) as a decimal is 0.8, and (9/5) as a decimal is 1.8.
Hence, you could also write the equation as y = 0.8x + 1.8, which is equivalent to y = (4/5)x + (9/5).