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How do you find the x and y intercepts of \[5x + 3y = 15\] ?

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Last updated date: 13th Jun 2024
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Answer
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Hint: In this question, we are given a linear equation that represents the equation of a line in the x-y plane and we have to find the x and y intercepts of this equation. We can find out the x and y intercepts of the line from its equation. The intercept form of the equation of a line is $\dfrac{x}{a} + \dfrac{y}{b} = 1$ where a is the x-intercept of this line ad b is the y-intercept of the line. We will first convert the given equation into the intercept form and then compare them. The given line is a straight line and all the points lying on the line will satisfy its equation.

Complete step by step solution:
The equation of the line given to us is \[5x + 3y = 15\] .
We will convert this equation into the standard equation of x and y-intercept form as follows –
\[
  \dfrac{{5x}}{{15}} + \dfrac{{3y}}{{15}} = 1 \\
   \Rightarrow \dfrac{x}{3} + \dfrac{y}{5} = 1 \\
 \]
On comparing this equation with the standard equation of x and y-intercept form $\dfrac{x}{a} + \dfrac{y}{b} = 1$ ,
We get –
$a = 3$ and $b = 5$

Hence the x-intercept of the given equation is 3, and the intercept of this equation is 5.

Note: The equation of a line can be written in various ways like slope-intercept form, intercept form etc. the x-intercept of a line is a point on the x-axis at which the line cuts the x-axis and the y-intercept is defined as a point on which the line cuts the y-axis. Thus, we can also find the x and y intercepts by putting the other point equal to zero.