Sure, let's walk through the detailed step-by-step solutions for the given questions.
### Question 4.3.1
"The line [tex]\( x = 0 \)[/tex] is described by...."
Firstly, we need to understand what the equation [tex]\( x = 0 \)[/tex] represents in a coordinate plane. This equation tells us that for all values of [tex]\( y \)[/tex], [tex]\( x \)[/tex] remains 0. Hence, this describes a vertical line that passes through the origin and upwards/downwards along the y-axis.
Given the options:
a) The x-axis
b) The y-axis
c) Any line through the origin.
Correct Option:
b) The y-axis
So, the line [tex]\( x = 0 \)[/tex] is described by the y-axis.
### Question 4.3.2
"In the relation [tex]\( y = mx + c \)[/tex],"
We need to identify the roles of [tex]\( m \)[/tex] and [tex]\( c \)[/tex] in the linear equation [tex]\( y = mx + c \)[/tex]. Here’s the breakdown:
- [tex]\( y = mx + c \)[/tex] is the slope-intercept form of a linear equation.
- [tex]\( m \)[/tex] represents the slope of the line, which indicates how steep the line is.
- [tex]\( c \)[/tex] represents the y-intercept, which is the point where the line crosses the y-axis.
Given the options:
a) m is the slope and c the x-intercept.
b) m is the slope and c the y-intercept.
c) c is the slope and m the x-intercept.
d) c is the slope and m the y-intercept.
Correct Option:
b) m is the slope and c the y-intercept.
So, in the relation [tex]\( y = mx + c \)[/tex], [tex]\( m \)[/tex] is the slope and [tex]\( c \)[/tex] the y-intercept.
We can now compile the results:
1. 4.3.1 - The line [tex]\( x = 0 \)[/tex] is described by the y-axis, which corresponds to option 2.
2. 4.3.2 - In the relation [tex]\( y = mx + c \)[/tex], [tex]\( m \)[/tex] is the slope and [tex]\( c \)[/tex] the y-intercept, which corresponds to option 2.
Therefore, the answers are:
- For question 4.3.1, the answer is 2.
- For question 4.3.2, the answer is 2.
