Question

How do you find the x and y intercept of $5x - y = 35$?

Answer 1

x-intercept can be found by substituting the value of ‘y’ is equal to zero in the given equation. Similarly we can find the y-intercept by substituting the value of ‘x’ equal to zero in the given equation. In other words ‘x’ intercept is defined as a line or a curve that crosses the x-axis of a graph and ‘y’ intercept is defined as a line or a curve crosses the y-axis of a graph.

Complete step-by-step solution:
Given, $5x - y = 35$.
To find the ‘x’ intercept put $y = 0$ in the above equation,
$\Rightarrow 5x - 0 = 35$
$\Rightarrow 5x = 35$
Divide by 5 on both sides of the equation,
$\Rightarrow x = \dfrac{{35}}{5}$
$\Rightarrow x = 7$.
Thus ‘x’ intercept is 7.
To find the ‘y’ intercept put $x = 0$ in the above equation,
$\Rightarrow 5(0) - y = 35$
$\Rightarrow - y = 35$
Multiply by $- 1$ on both sides of the equation,
$\Rightarrow y = - 35$.
Thus ‘y’ intercept is $- 35$.

Note: We can solve this using the standard intercept form. That is the equation of line which cuts off intercepts ‘a’ and ‘b’ respectively from ‘x’ and ‘y’ axis is $\dfrac{x}{a} + \dfrac{y}{b} = 1$. We convert the given equation into this form and compare it will have a desired result.
Given $5x - y = 35$
Now we need 1 on the right hand side of the equation, so divide the whole equation by 35. We have,
$\dfrac{{5x - y}}{{35}} = \dfrac{{35}}{{35}}$
Splitting the terms we have,
$\Rightarrow \dfrac{{5x}}{{35}} - \dfrac{y}{{35}} = \dfrac{{35}}{{35}}$
$\Rightarrow \dfrac{x}{7} - \dfrac{y}{{35}} = 1$
That is we have,
$\Rightarrow \dfrac{x}{7} + \dfrac{y}{{ - 35}} = 1$. On comparing with standard intercept form we have ‘x’ intercept is 7 and y intercept is $- 35$. In both the cases we have the same answer.