Sure, let's solve the given problems step-by-step.
### Part 1
#### (1a) Find the slope and [tex]\( y \)[/tex]-intercept of the line given by the equation [tex]\( x - 8y - 24 = 0 \)[/tex].
Step 1: Rewrite the equation in slope-intercept form [tex]\( y = mx + c \)[/tex], where [tex]\( m \)[/tex] is the slope and [tex]\( c \)[/tex] is the [tex]\( y \)[/tex]-intercept.
The given equation is:
[tex]\[ x - 8y - 24 = 0 \][/tex]
Step 2: Solve for [tex]\( y \)[/tex]:
[tex]\[ x - 24 = 8y \][/tex]
[tex]\[ y = \frac{1}{8}x - 3 \][/tex]
From this equation, we can see that:
- The slope [tex]\( m \)[/tex] is [tex]\( \frac{1}{8} \)[/tex] or [tex]\( 0.125 \)[/tex].
- The [tex]\( y \)[/tex]-intercept [tex]\( c \)[/tex] is [tex]\( -3 \)[/tex].
So, the slope is [tex]\( 0.125 \)[/tex] and the [tex]\( y \)[/tex]-intercept is [tex]\( -3 \)[/tex].
#### (1b) Find the slope and [tex]\( y \)[/tex]-intercept of the line given by the equation [tex]\( y = \sqrt{3}x + 3 \)[/tex].
This equation is already in the slope-intercept form [tex]\( y = mx + c \)[/tex].
From this equation, we can see that:
- The slope [tex]\( m \)[/tex] is [tex]\( \sqrt{3} \)[/tex], which is approximately [tex]\( 1.732 \)[/tex].
- The [tex]\( y \)[/tex]-intercept [tex]\( c \)[/tex] is [tex]\( 3 \)[/tex].
So, the slope is approximately [tex]\( 1.732 \)[/tex] and the [tex]\( y \)[/tex]-intercept is [tex]\( 3 \)[/tex].
### Part 2
#### Find the equation of the given straight line [tex]\( AB \)[/tex].
I see that the second part of your question is incomplete, and additional information such as the coordinates of points [tex]\( A \)[/tex] and [tex]\( B \)[/tex] is required to find the equation of the line [tex]\( AB \)[/tex]. If you could provide these points or any other necessary information, I can help you derive the equation for the line [tex]\( AB \)[/tex].
If you have any further questions or need additional assistance, please let me know!
