Question

How do you find the x-intercept of the $4x+5y+6=0$ ?

Answer 1

In order to solve the solve question, first we need to convert the given linear equation in the standard slope intercept form of a linear equation by simplifying the given equation. The slope intercept form of a linear equation is, $y=mx+b$, where ‘m’ is the slope of the line and ‘b’ is the y-intercept. Then for x-intercept, we need to put the value of y = 0 and solve for the value of ‘x’. in this way we will get all required values.

Complete step by step answer:
We have given that,
$4x+5y+6=0$
As we know that the slope intercept form of a linear equation is,
$y=mx+b$, where ‘m’ is the slope of the line and ‘b’ is the y-intercept.
Converting the given equation in slope intercept form of equation;
$4x+5y+6=0$
Subtracting 6 from both the sides of equation, you get
$4x+5y=-6$
Subtracting 4x from both the sides of equation, you get
$5y=-6-4x$
Dividing both the sides of the equation by 5, we get
$y=-\dfrac{6}{5}-\dfrac{4}{5}x$
Rewrite the above equation as,
$y=-\dfrac{4}{5}x-\dfrac{6}{5}$
Comparing it with the slope intercept form of a linear equation i.e. $y=mx+b$
Thus,
Slope = m = 6
Y-intercept = b = 10
Now,
Finding the x-intercept,
We need to put the value of y = 0,
We have,
$y=-\dfrac{4}{5}x-\dfrac{6}{5}$
$\Rightarrow 0=-\dfrac{4}{5}x-\dfrac{6}{5}$
Adding $\dfrac{6}{5}$ to both the sides of the equation, we get
$\dfrac{6}{5}=-\dfrac{4}{5}x$
Multiply both the sides by 5, we get
$6=-4x$
Dividing both the side of equation by -4, we get
$\therefore x=-\dfrac{6}{4}=-\dfrac{3}{2}$

Therefore, the x-intercept is $-\dfrac{3}{2}$.

Note: While solving these types of questions, students need to know the concept of slope intercept form of linear equation. Solve the equation very carefully and do the calculation part very explicitly to avoid making any errors. They should be well aware about the concept of finding the intercept when given parabola, quadratic equation, vertex form etc.