Question

Find the x-intercept and y-intercept of the line.6x – 4y= 21-Write your answers as exact values. Do not write your answers as ordered pairs.x-intercept: y-intercept:

Answer 1

The x-intercept, is the x-value when the function "cuts" the x-axis, when y = 0. To find the x-intercept we just need to evaluate the function at y = 0.

$\begin{gathered} 6x-4\cdot0=21 \\ \Rightarrow x=\frac{21}{6}=\frac{7}{3} \end{gathered}$

The y-intercept follows the same idea, then, we just need to evaluate the function at x = 0.

$6\cdot0-4y=21\Rightarrow y=-\frac{21}{4}$

Then, our intercepts are:

$\begin{gathered} x-\text{intercept}=\frac{7}{3} \\ y-\text{intercept}=-\frac{21}{4} \end{gathered}$