Question

How do you find the x and y intercepts for $ 4x + 5y = 20 $

Answer 1

Hint: An intercept is the distance between the point where the curve crosses the x or y axis and the origin. If the curve passes through the x axis, then the distance between the origin and the intersection point on the x axis is called x intercept and similarly for y intercept.

Complete step-by-step answer:
Given to us is an equation of a curve $ 4x + 5y = 20 $
This curve cuts the x axis and y axis at a point each. When this curve meets the x axis, the value of y coordinate will be zero at that particular intersection point. So the coordinates of the x intercept would be $ \left( {X,0} \right) $
This point lies on the curve so it must satisfy the curve equation. Hence let us now substitute this point in the given curve equation.
 $ 4X + 5\left( 0 \right) = 20 $
On solving, we get $ X = \dfrac{{20}}{4} = 5 $
Hence the x intercept is $ 5 $
Similarly, when the curve meets the y axis, the value of x coordinate will be zero at that intersection point and hence we can write the coordinates of the y intercept as $ \left( {0,Y} \right) $
This point lies on the curve so we can substitute this point in the given equation to get $ 4\left( 0 \right) + 5Y = 20 $
On solving, we get $Y = \dfrac{{20}}{5} = 4 $
Therefore, the y intercept is $ 4 $
So, the correct answer is “4”.

Note: It is to be noted that we can also write the intercept points for both x and y axis. The intercept point for x axis would be $ \left( {5,0} \right) $ since the x intercept is $ 5 $ and similarly the intercept point for y axis would be $ \left( {0,4} \right) $ since the y intercept is $ 4 $