Answer
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Hint: 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. 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 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 $y = - 3x + 6$ .It can be rewritten as –
\[3x + y = 6\] .
We will convert this equation into the standard equation of x and y-intercept form as follows –
\[
\dfrac{{3x}}{6} + \dfrac{y}{6} = 1 \\
\Rightarrow \dfrac{x}{2} + \dfrac{y}{6} = 1 \\
\]
On comparing this equation with the standard equation of x and y-intercept form $\dfrac{x}{a} + \dfrac{y}{b} = 1$ ,
We get –
$a = 2$ and $b = 6$
Hence the x-intercept of the given equation is 2, and the intercept of this equation is 6.
Note: 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 can also find the x and y intercepts by putting the other point equal to zero. This way we can solve similar questions.
Complete step by step solution:
The equation of the line given to us is $y = - 3x + 6$ .It can be rewritten as –
\[3x + y = 6\] .
We will convert this equation into the standard equation of x and y-intercept form as follows –
\[
\dfrac{{3x}}{6} + \dfrac{y}{6} = 1 \\
\Rightarrow \dfrac{x}{2} + \dfrac{y}{6} = 1 \\
\]
On comparing this equation with the standard equation of x and y-intercept form $\dfrac{x}{a} + \dfrac{y}{b} = 1$ ,
We get –
$a = 2$ and $b = 6$
Hence the x-intercept of the given equation is 2, and the intercept of this equation is 6.
Note: 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 can also find the x and y intercepts by putting the other point equal to zero. This way we can solve similar questions.