Question

How do you find the intercepts for \[7x + 2y = 28\] ?

Answer 1

Hint:Here we need to find ‘x’ and ‘y’ intercepts. 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 answer:
Given, \[7x + 2y = 28\].
To find the ‘x’ intercept put \[y = 0\] in the above equation,
\[7x + 2(0) = 28\]
\[ \Rightarrow 7x = 28\]
Divide by 7 on both sides of the equation,
\[x = \dfrac{{28}}{7}\]
\[ \Rightarrow x = 4\].
Thus ‘x’ intercept is 4.

To find the ‘y’ intercept put \[x = 0\] in the above equation,
\[7(0) + 2y = 28\]
\[2y = 28\]
Divide by 2 on both sides of the equation,
\[y = \dfrac{{28}}{2}\]
\[ \Rightarrow y = 14\].
Thus ‘y’ intercept is 14. If we draw the graph for the above equation. We will have a line or curve that crosses the x-axis at 4 and y-axis at 14.

Hence,‘x’ intercept is 4 and ‘y’ intercept is 14.

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 \[7x + 2y = 28\]
Now we need 1 on the right hand side of the equation, so divide the whole equation by 28. We have,
\[\dfrac{{7x + 2y}}{{28}} = \dfrac{{28}}{{28}}\]
Splitting the terms we have,
\[\dfrac{{7x}}{{28}} + \dfrac{{2y}}{{28}} = \dfrac{{28}}{{28}}\]
That is we have,
\[\dfrac{x}{4} + \dfrac{y}{{14}} = 1\]
On comparing with standard intercept form we have ‘x’ intercept is 4 and y intercept is 14. In both the cases we have the same answer.