Question

How do you find the intercepts for $y = 8x - 3$ ?

Answer 1

Hint: Intercepts are the points on the X-axis and Y-axis where a line intersects the axis. Hence to find the intercept on the respective axis we need to consider the other variable as zero and find the value of that variable. For Y-intercept, we consider $x = 0$ and find the value of $y$ .

Complete step-by-step answer:
Intercepts are the points on the X-axis and the Y-axis where a line intersects or cuts through.
Not every line needs to have an intercept on both axes.
If a line is horizontal or vertical then it either has an X-intercept or a Y-intercept, it cannot have both.
If a line passes through the origin, then it doesn’t have any intercept on the axis.
To find an intercept on any axis, we need to consider the other coordinate as zero and from the equation, find the value of that coordinate.
Thus for Y-intercept, we need to consider the X-coordinate $x = 0$ and substitute this value in the equation of the line and calculate the value of Y-intercept.
Similarly for X-intercept, we need to consider the Y-coordinate $y = 0$ and substitute this value in the equation of the line and calculate the value of the X-intercept.
Here, the equation of the line is $y = 8x - 3$ .
To find the X-intercept, let’s consider the Y coordinate $y = 0$ .
Substituting $y = 0$ in the equation of the line
$ \Rightarrow 0 = 8x - 3$
Making $x$ as the subject of the equation
$ \Rightarrow 8x = 3$
$ \Rightarrow x = \dfrac{3}{8}$
Hence, the X-intercept of the line is $x = \dfrac{3}{8}$ or $(\dfrac{3}{8},0)$ .
Similarly, for the Y-intercept, let’s consider the X coordinate $x = 0$ .
Substituting $x = 0$ in the equation of the line
$ \Rightarrow y = 8(0) - 3$
$ \Rightarrow y = - 3$
Hence, the Y-intercept of the line is $y = - 3$ or $(0, - 3)$ .

Hence, the intercepts of the line $y = 8x - 3$ are $(\dfrac{3}{8},0)$ and $(0, - 3)$.

Note:
The intercepts can also be found using the line equation $y = mx + c$ , where $m$ is the slope of the line and $c$ is the Y-intercept. Similarly for the line equation $x = my + b$, where $m$ is the slope of the line and $b$ is the X-intercept.