Sure! Let's find the [tex]\( x \)[/tex]-intercept and [tex]\( y \)[/tex]-intercept for the equation [tex]\( \frac{3}{4} x - 3 y = 1 \)[/tex].
### Finding the [tex]\( x \)[/tex]-intercept
To find the [tex]\( x \)[/tex]-intercept, we set [tex]\( y = 0 \)[/tex] in the equation and solve for [tex]\( x \)[/tex].
[tex]\[ \frac{3}{4} x - 3 (0) = 1 \][/tex]
This simplifies to:
[tex]\[ \frac{3}{4} x = 1 \][/tex]
To solve for [tex]\( x \)[/tex], we multiply both sides of the equation by [tex]\(\frac{4}{3}\)[/tex]:
[tex]\[ x = 1 \times \frac{4}{3} = \frac{4}{3} \][/tex]
Therefore, the [tex]\( x \)[/tex]-intercept is [tex]\( \left( \frac{4}{3}, 0 \right) \)[/tex].
### Finding the [tex]\( y \)[/tex]-intercept
To find the [tex]\( y \)[/tex]-intercept, we set [tex]\( x = 0 \)[/tex] in the equation and solve for [tex]\( y \)[/tex].
[tex]\[ \frac{3}{4} (0) - 3 y = 1 \][/tex]
This simplifies to:
[tex]\[ -3 y = 1 \][/tex]
To solve for [tex]\( y \)[/tex], we divide both sides of the equation by [tex]\(-3\)[/tex]:
[tex]\[ y = \frac{1}{-3} = -\frac{1}{3} \][/tex]
Therefore, the [tex]\( y \)[/tex]-intercept is [tex]\( \left( 0, -\frac{1}{3} \right) \)[/tex].
### Summary
- The [tex]\( x \)[/tex]-intercept is [tex]\( \left( \frac{4}{3}, 0 \right) \)[/tex].
- The [tex]\( y \)[/tex]-intercept is [tex]\( \left( 0, -\frac{1}{3} \right) \)[/tex].
