Question

How do you find the x and y- intercepts for $- 4x - 7y + 7 = 0$?

Answer 1

In this question we have to find the x and y intercepts of the given line, first we have to convert the given equation into the double intercept form which is given by $\dfrac{x}{a} + \dfrac{y}{b} = 1$, where $a$ is the x-intercept and $b$ is the y-intercept of the line, now after transforming the given equation compare the equation with the double intercept form, then we will get the required intercepts.

Complete step by step solution:
Given equation of the line is $- 4x - 7y + 7 = 0$,
Now we have to convert the equation into the double intercept form which is given by $\dfrac{x}{a} + \dfrac{y}{b} = 1$, where $a$ is the x-intercept and $b$is the y-intercept of the line,
Given equation is $- 4x - 7y + 7 = 0$,
Now subtract 7 from both sides of the equation we get,
$\Rightarrow - 4x - 7y + 7 - 7 = 0 - 7$,
Now simplifying we get,
$\Rightarrow - 4x - 7y = - 7$,
Now divide both sides with -7 we get,
$\Rightarrow \dfrac{{ - 4x}}{{ - 7}} - \dfrac{{7y}}{{ - 7}} = \dfrac{{ - 7}}{{ - 7}}$,
Now simplifying we get,
$\Rightarrow \dfrac{{4x}}{7} + y = 1$,
Now divide numerator and denominator of the term $\dfrac{{4x}}{7}$ with 4, we get,
$\Rightarrow \dfrac{{\dfrac{{4x}}{4}}}{{\dfrac{7}{4}}} + y = 1$,
Now simplifying we get,
$\Rightarrow \dfrac{x}{{\dfrac{7}{4}}} + \dfrac{y}{1} = 1$,
Now comparing the equation with $\dfrac{x}{a} + \dfrac{y}{b} = 1$, we get,
So, here $a=\dfrac{7}{4}$ and $b = 1$,
Now the x-intercept is $\dfrac{7}{4}$ and y-intercept is 1.

$\therefore$The x and y- intercepts of the given line $- 4x - 7y + 7 = 0$ are $\dfrac{7}{4}$ and 1.

Note: Another method of finding the intercepts is ,
To find the y-intercept of the line, the value of $x$ should be taken as 0 in the equation of line, so the equation of the line is given as
$\Rightarrow - 4x - 7y + 7 = 0$,
Now substitute in the equation, we get,
$\Rightarrow - 4\left( 0 \right) - 7y + 7 = 0$,
Now simplifying we get,
$\Rightarrow 0 - 7y + 7 = 0$
Again simplifying we get,
$\Rightarrow - 7y + 7 = 0$
Now add 7y from both sides of the equation we get,
$\Rightarrow - 7y + 7 + 7y = 0 + 7y$,
Now simplifying we get,
$\Rightarrow 7 = 7y$,
Now divide both sides with 7 we get,
$\Rightarrow \dfrac{{7y}}{7} = \dfrac{7}{7}$,
Now simplifying we get,
$\Rightarrow y = 1$,
So, y-intercept will be 1.
Now to find the x-intercept of the line, the value of $y$ should be taken as 0 in the equation of line, so the equation of the line is given as
$\Rightarrow - 4x - 7y + 7 = 0$,
Now substitute $y = 0$ in the equation, we get,
$\Rightarrow - 4x - 7\left( 0 \right) + 7 = 0$,
Now simplifying we get,
$\Rightarrow - 4x - 0 + 7 = 0$,
Again simplifying we get,
$\Rightarrow - 4x + 7 = 0$,
Now add 4x from both sides of the equation we get,
$\Rightarrow - 4x + 7 + 4x = 0 + 4x$,
Now simplifying we get,
$\Rightarrow 7 = 4x$,
Now divide both sides with 4 we get,
$\Rightarrow \dfrac{{4x}}{4} = \dfrac{7}{4}$,
Now simplifying we get,
$\Rightarrow x = \dfrac{7}{4}$,
So x-intercept will be $\dfrac{7}{4}$,
Which is the same as above, so we got the same result in two ways.