Question

How do you give only the x-intercept of $6x-3y=-24$ ?

Answer 1

The x-intercept is the point where the y coordinate of the point is equal to zero and y-intercept is the point where the x coordinate of the point is equal to zero. To find x intercept substitute $y=0$ in the given equation.

Complete step by step solution:
They can write the given equation as $6x-3y+24=0$ …. (i)
We can see that the given equation is the general form of the equation of a straight line.
I.e. $ax+by+c=0$, where a, b and c are real numbers.
Therefore, we have confirmed that the given equation is an equation of a straight line.
The x-intercept of a line is the point where the straight line cuts or meets the x-axis This means that x-intercept is the point where the y coordinate of the point is equal to zero Therefore,
Now, substitute $y=0$ in equation (i).
Then,
$\Rightarrow 6x-3(0)+24=0$
$\Rightarrow x=-4$
This means that the x intercept for the given line is $\left( 2,0 \right)$.

Note:
There is another method to find the x and y intercepts of a line and that is by writing the given equation of line in intercepts form.
The intercept form of line is given as $\dfrac{x}{a}+\dfrac{y}{b}=1$.
Where a and b are x and y intercepts respectively.