Question

How do you find the x and y intercept of \[5x - y = 35\]?

Answer 1

Hint: 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.