To determine the points where the line represented by the equation [tex]\( 4x - 3y = -4 \)[/tex] intersects the x-axis and y-axis, we need to find both the x-intercept and the y-intercept.
### Finding the x-intercept:
1. The x-intercept is the point where the line crosses the x-axis. At this point, the value of [tex]\( y \)[/tex] is 0.
2. Set [tex]\( y = 0 \)[/tex] in the equation [tex]\( 4x - 3y = -4 \)[/tex]:
[tex]\[
4x - 3(0) = -4
\][/tex]
Simplifying this equation, we have:
[tex]\[
4x = -4
\][/tex]
3. Solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{-4}{4} = -1
\][/tex]
4. Therefore, the x-intercept is at the point [tex]\( (-1, 0) \)[/tex].
### Finding the y-intercept:
1. The y-intercept is the point where the line crosses the y-axis. At this point, the value of [tex]\( x \)[/tex] is 0.
2. Set [tex]\( x = 0 \)[/tex] in the equation [tex]\( 4x - 3y = -4 \)[/tex]:
[tex]\[
4(0) - 3y = -4
\][/tex]
Simplifying this equation, we have:
[tex]\[
-3y = -4
\][/tex]
3. Solve for [tex]\( y \)[/tex]:
[tex]\[
y = \frac{-4}{-3} = \frac{4}{3}
\][/tex]
4. Therefore, the y-intercept is at the point [tex]\( \left(0, \frac{4}{3}\right) \)[/tex].
### Conclusion:
The points where the line intersects the x-axis and y-axis are:
- x-intercept: [tex]\( (-1, 0) \)[/tex]
- y-intercept: [tex]\( \left(0, \frac{4}{3}\right) \)[/tex]
These points represent the locations where the line [tex]\( 4x - 3y = -4 \)[/tex] meets each axis.
