Question

# The intercepts on the coordinate axes of the straight line with the given equation displaystyle{4}{x}-{3}{y}={12}.

Alternate coordinate systems
The intercepts on the coordinate axes of the straight line with the given equation $$\displaystyle{4}{x}-{3}{y}={12}.$$

2021-02-26
Concept used:
If a straight line passes through the points (a, 0) (on the x-axis) and (0, b) (on the y-axis), we say that the x-intercept is a and the y-intercept is
b.
The x -intercept is found by setting $$\displaystyle{y}={0}$$ and solving for a, similarly, the y-intercept is found by setting $$\displaystyle{x}={0}$$ and solving for b.
Calculation:
For the given equation $$\displaystyle{4}{x}-{3}{y}={12}$$
$$\displaystyle{y}={0}\Rightarrow{4}{x}={12}\Rightarrow{x}-\text{intercept}={3},$$
$$\displaystyle{x}={0}\Rightarrow-{3}{y}={12}\Rightarrow{y}-\text{intercept}=-{4}$$
Conclusion:
For the given line, $$\displaystyle{x}-\text{intercept}={3}{\quad\text{and}\quad}{y}-\text{intercept}=-{4}$$