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 $4$