Question

How do you find the $ x $ and $ y $ intercept of $ x - 2y = - 10? $

Answer 1

Hint: In this problem we have given an equation and here we are asked to find the $ x $ and $ y $ intercept of the given equation and geometrically to solve this problem we need to substitute some value for $ x $ to find the $ x $ intercept and also substitute one value for $ y $ to find the $ y $ intercept.

Complete step-by-step solution:
Given equation is $ x - 2y = - 10 $
There are two axes in the graph. In that, $ X $ intercept is the value of $ x $ when the value of $ y $ is equal to zero.
This implies that, when we substitute the value of $ y $ is equal to zero the given equation becomes,
 $ x - 2(0) = - 10 $
Multiplication of any number with zero is again zero. So the above equation becomes,
 $ x - 0 = - 10 $
 $ \Rightarrow x = - 10 $
So, $ X $ intercept is $ x = - 10 $ .
Now, $ Y $ intercept is the value of $ y $ when the value of $ x $ is equals to zero.
This implies that, when we substitute the value of $ x $ is equal to zero the given equation becomes,
 $ 0 - 2y = - 10 $
 $ \Rightarrow - 2y = - 10 $
Keep the $ y $ term in the left hand side,
 $ \Rightarrow y = \dfrac{{ - 10}}{{ - 2}} $ , after cancelling we get
 $ \Rightarrow y = 5 $
So, $ Y $ intercept is $ y = 5 $

The x intercept is equal to -10 and y intercept is equal to 5.

Note: When the line crosses the $ x $ axis the $ y $ coordinate at the point will be zero. By substituting $ y = 0 $ into the equation we will obtain the $ x $ -intercept. Similarly, when the line crosses the $ y $ axis the $ x $ coordinate at this point will be zero. Substituting $ x = 0 $ into the equation will give us the $ y $ -intercept. Let us explain this by plotting a graph.

The intercepts of a graph are points at which the graph crosses the axes. The $ x $ -intercept is the point at which the graph crosses the $ x $ -axis. At this point, the $ y $ -coordinate is zero. The $ y $ -intercept is the point at which the graph crosses the $ y $ -axis. At this point, the $ x $ -coordinate is zero.