Question

What is the y-intercept of $2x-5y=35$?

Answer 1

Hint: To find the y-intercept of $2x-5y=35$, we are going to put the value of x as 0 in the given equation of the straight line and then solve this equation where we have put the value of x as 0 and then solve the value of y. The value of y which we have solved in the above equation is the y-intercept.

Complete step-by-step answer:
The equation of the straight line given in the above problem is as follows:
$2x-5y=35$
And we are asked to write the y-intercept for the above equation which we are going to do by substituting the value of x as 0 in the above equation and then solve that equation.
$\begin{align}
  & 2\left( 0 \right)-5y=35 \\
 & \Rightarrow 0-5y=35 \\
\end{align}$
Dividing 5 on both the sides of the above equation we get,
$-\dfrac{5y}{5}=\dfrac{35}{5}$
In the L.H.S of the above equation, 5 will get cancelled out from the numerator and the denominator and in the R.H.S, the division of 35 by 5 will give 7 as the quotient.
$\Rightarrow -y=7$
Now, to remove the negative sign in front of y we are going to multiply -1 on both the sides of the above equation and we get,
$y=-7$
Now, the value of y which we are getting by putting x as 0 is the y-intercept of the given equation of the straight line.
Hence, the y-intercept of the given equation is -7.

Note: The alternate approach to find the y-intercept is by writing the given straight line equation in the slope-intercept form of a straight line which is as follows:
The slope-intercept form for the straight line equation is written in the following way:
$y=mx+c$
Now, rearranging the given equation in the above form and get the value of m and c we get,
The equation of the straight line is as follows:
$2x-5y=35$
Now, adding 5y on both the sides of the above equation we get,
$2x=5y+35$
Subtracting 35 on both the sides of the above equation we get,
$2x-35=5y$
Now, dividing 5 on both the sides of the above equation we get,
$\dfrac{2x-35}{5}=y$
Distributing 5 written in the denominator to 2x and 35 we get,
$\begin{align}
  & \dfrac{2x}{5}-\dfrac{35}{5}=y \\
 & \Rightarrow \dfrac{2x}{5}-7=y \\
\end{align}$
Rearranging the above equation we get,
$\Rightarrow y=\dfrac{2x}{5}-7$
Now, comparing the above equation with standard slope-intercept form $y=mx+c$ we get,
$y=\dfrac{2x}{5}-7$
$y=mx+c$
The value of m is $\dfrac{2x}{5}$ and value of c is -7 and “c” is the y-intercept so the y-intercept is -7.