Question

How do you find the x and y intercept of $3x + 0.5y = 6?$

Answer 1

Hint: Intercept can be defined as the line which intersects the x-axis or the y-axis. In the standard formula $y = mx + b$ where b is the intercept of the given equation. There is y-intercept when x is equal to zero and x-intercept when y is equal to zero.

Complete step by step answer:
First of all we will find the “x” intercepts which occur on “x” axis when $y = 0$, so find the value for x.
Take the given expression: $3x + 0.5y = 6$
Place $y = 0$in the above equation.
$3x = 6$
Now, take the coefficient on the opposite side and make the subject “x”. term multiplicative on one side if moved to the opposite side then it goes to the denominator.
$ \Rightarrow x = \dfrac{6}{3}$
Common factor from the numerator and the denominator cancel each other.
$ \Rightarrow x = 2$
So, the x-intercept is at the origin $(2,0)$ ….. (A)
Now, similarly for the y intercepts when $x = 0$
Take the given expression: $3x + 0.5y = 6$
Place $x = 0$ in the above equation.
$3(0) + 0.5y = 6$
Simplify the above equation and also apply that when zero is multiplied with any number gives zero as the resultant value.
$0.5y = 6$
Make “y” the subject –
$y = \dfrac{6}{{0.5}}$
Simplify the above equation –
$ \Rightarrow y = 12$
So, the y-intercept is at the origin $(0,12)$ … (B)
Hence, the equations (A) and (B) are the required solution.

Additional Information:
In any linear equation, m is the slope and b is the y-intercept and this equation is known as the slope-intercept equation.

Note: Always remember the standard form of the linear equation, slope and intercept equation as the y intercept depends on the standard equation. Also, know the basic identities to simplify the equation such as zero when multiplied with any number always gives the resultant value as zero.