Question

How do you find the slope and $y$ intercept of $5x - 2y - 7 = 0$ ?

Answer 1

Hint: In this problem, we are given a linear equation and we have been asked to find the slope of the given equation and also $y$ intercept of the given equation. We are going to use the slope formula to find the slope and $y$ intercept of the given equation.

Formula used: The equation of any straight line, called a linear equation, can be written as $y = mx + b$ , where $m$ is the slope of the line and $b$ is the $y$ - intercept.

Complete step-by-step solution:
Given equation is $5x - 2y - 7 = 0$
Now we are going to solve this given equation for $y$ .
Subtract $5x$ from both sides of the given equation, we get,
$ \Rightarrow 5x - 2y - 7 - 5x = 0 - 5x$
On the left-hand side, both $ - 5x$ and $ + 5x$ get canceled by each other.
$ \Rightarrow - 2y - 7 = 0 - 5x$
If we subtract anything from zero then we get the same answer.
$ \Rightarrow - 2y - 7 = - 5x$ ………………... (1)
Now add $7$to both sides of equation (1), we get,
$ \Rightarrow - 2y - 7 + 7 = - 5x + 7$
Here, on the left-hand side, both $ - 7$ and $ + 7$ get canceled by each other. Then we get,
$ \Rightarrow - 2y = - 5x + 7$
Now, let’s multiply every term of the above equation by $ - 1$ , we get
$ \Rightarrow ( - 1)( - 2y) = ( - 1)( - 5x) + 7( - 1)$
$ \Rightarrow 2y = 5x - 7$ ………….…. (2)
Divide both sides by $ - 2$ in the equation (2), we get
$ \Rightarrow \dfrac{{2y}}{2} = \dfrac{{5x}}{2} - \dfrac{7}{2}$,
On the left-hand side, $2$ is in both numerator and denominator. So, it cancels each other, we get
$ \Rightarrow y = \dfrac{{5x}}{2} - \dfrac{7}{2}$ …………... (3)
Now, the equation (3) is in slope – intercept form $y = mx + b$, where $m$ is the slope of the line and $b$ is the $y$ - intercept.

Then for equation $y = \dfrac{5}{2}x - \dfrac{7}{2}$, the slope is $\dfrac{5}{2}$ and the $y$-intercept is $ - \dfrac{7}{2}$.

Note: Always $y$ intercept of any line is the value of $y$ at the point where the line crosses the $y$ axis and will always appear as $\left( {0,b} \right)$ in coordinate form. Here, by using the slope intercept formula we found the value of slope and $y$-intercept. The slope indicates the rate of change in $y$ per unit in $x$ . The $y$ intercept indicates the $y$ -value when the $x$ -value is zero.