Question

How do you find the slope of \[3x+y=5\]?

Answer 1

Hint: From the question given, we have been asked to find the slope of \[3x+y=5\]. We can find the slope of the above-given equation from the question by simply rearranging the equation. We have to rearrange the equation into slope-intercept form. After rearranging it into the slope-intercept form, we can get the slope of the given equation.

Complete step by step answer:
For answering this question we will consider the line equation given in the question.
First of all, we need to know about the slope-intercept form.
Slope-intercept form: \[y=mx+b\] where, \[m\] is the slope of the line equation and \[b\] is the \[y\]-intercept.
Now, as we have been already discussed above, we have to rearrange the given equation into slope-intercept form.
From the question, the given line equation is \[3x+y=5\]
Shift \[3x\] from the left hand side of the equation to the right-hand side of the equation.
By shifting \[3x\] from the left hand side of the equation to the right-hand side of the equation, we get \[y=-3x+5\]
We can clearly observe that the above equation is in the form of \[y=mx+b\] that is slope-intercept form.
So, by comparing the coefficients of both the equations, we get \[m=-3\]
Therefore, the slope of the given equation is \[m=-3\].

Note:
We should be well aware of the slope of the line. Also, we should be well known about the slope intercept form. Also, we should be very careful while converting the given line equation into the slope intercept form. After rearranging the given line equation into slope intercept form, we should carefully observe the coefficients of both the equations to get the slope of the given line equation. The slope of this line can be found by using the equation $ m=\dfrac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}} $ where $ \left( {{x}_{1}},{{y}_{1}} \right) $ and $ \left( {{x}_{2}},{{y}_{2}} \right) $ are the points lying on the line. For the line $ 3x+y=5 $ , the points $ \left( 0,5 \right) $ and $ \left( \dfrac{5}{3},0 \right) $ the slope of the line is given as $ m=\dfrac{0-5}{\dfrac{5}{3}-0}=\dfrac{-5}{\dfrac{5}{3}}=-3 $