Question

How do you find the x and y intercept of \[y = 3x - 2\]?

Answer 1

Hint: Consider a straight line equation $Ax + By = C$.
To find the x-intercept, substitute \[y = 0\] and solve for $x$.
To find the y-intercept, substitute \[x = 0\] and solve for $y.$

Complete step-by-step solution:
Equation of the line given is \[y = 3x - 2\]
For x-intercept, substituting \[y = 0\]
\[ \Rightarrow 3x - 2 = 0\]
To find the value of $x$
\[ \Rightarrow 3x = 2\]
Dividing both sides by\[3\] , we get
\[ \Rightarrow \dfrac{{3x}}{3} = \dfrac{2}{3}\]
To get the value of $x$
\[ \Rightarrow x = \dfrac{2}{3}\]
For y-intercept, substituting \[x = 0\]
\[y = 3x - 2\]
Put the value of $x$
\[ \Rightarrow y = 3(0) - 2\]
\[ \Rightarrow y = - 2\]

Therefore x-intercept is \[\dfrac{2}{3}\] and y-intercept is -2.

Note: An intercept is a point on the $y$-axis, through which the slope of the line passes. It is $y$-coordinate of a point where a straight line or a curve intersects the y-axis. This is represented when we write the equation of a line, $y = mx + c$, where m is slope and $c$ is the $y$-intercept.
There are basically two intercepts, $x$-intercept and $y$-intercept. The point where the line crosses the $x$-axis is the $x$-intercept and the point where the line crosses the $y$-axis is the $y$-intercept.
Definition
The point where the line or curve crosses the axis of the graph is called intercept. If a point crosses the $x$-axis, then it is called $x$-intercept. If a point crosses the $y$-axis, then it is called $y$-intercept.