Question

How do you find the slope for \[2x+y=7\]?

Answer 1

Hint: Write the given equation in slope-intercept form. To do this, keep the variable y in the L.H.S. and take all other terms to the R.H.S. Now, make the coefficient of y equal to 1 and compare the obtained equation with \[y=mx+c\]. Here, ‘m’ will be the slope of the line and ‘c’ will be its intercept.

Complete step by step answer:
Here, we have been provided with the linear equation \[2x+y=7\] and we have been asked to find the slope of this line. But first, we need to know about the slope-intercept form of a linear equation.
Now, we know that we can write a linear equation of a straight line in many forms like - standard form, slope-intercept form, polar form, parametric form, etc. But here we need to see the slope-intercept form.
In the slope-intercept form, we write the equation of a line as: - \[y=mx+c\], where ‘m’ represents the slope and ‘c’ represents the intercept on y-axis. Here, we have been provided with the equation: - \[2x+y=7\]. So, keeping the term containing the variable ‘y’ in the L.H.S. and taking all other terms to the R.H.S., we get,
\[\Rightarrow y=7-2x\]
\[\Rightarrow y=-2x+7\] - (1)
Now, when we compare equation (1) with the relation \[y=mx+c\], we can conclude that we have,
\[\Rightarrow \] Slope of the given line = m = -2.
Hence, -2 is the slope and our answer.

Note:
One may note that here the coefficient of y was already 1 and that is why we did not require any arithmetic operation to simplify it. Remember that if the coefficient of y would have been any numerical value other than 1 then we need to convert it into 1 first. Generally, you can also remember the direct formula for the slope of a line of the form \[ax+by+c=0\] given as \[m=\dfrac{-b}{a}\]. In the above question, you can also determine the intercept, it is 7 units.