Let's break down the information provided and complete the table step-by-step.
### Step-by-Step Solution:
1. Row a):
- Given:
- Gradient ([tex]\(m\)[/tex]): -1
- [tex]\(y\)[/tex]-intercept ([tex]\(c\)[/tex]): -1
- Equation form is [tex]\( y = mx + c \)[/tex]
- Substitute the values into the equation:
[tex]\[
y = -1x + (-1)
\][/tex]
- Simplify the equation:
[tex]\[
y = -1x - 1
\][/tex]
So, the completed entry for row a) is:
[tex]\[
\text{a)} \quad m = -1, \quad c = -1, \quad \text{Equation: } y = -1x - 1
\][/tex]
2. Row b):
- It states:
- Equation is [tex]\( y = -6 \)[/tex]
- This implies a horizontal line with:
- Gradient ([tex]\(m\)[/tex]): 0
- [tex]\(y\)[/tex]-intercept ([tex]\(c\)[/tex]): -6
So, the completed entry for row b) is:
[tex]\[
\text{b)} \quad m = 0, \quad c = -6, \quad \text{Equation: } y = -6
\][/tex]
3. Row d) [first entry]:
- Given:
- Gradient ([tex]\(m\)[/tex]): 0
- [tex]\(y\)[/tex]-intercept ([tex]\(c\)[/tex]): -3
- Equation form is [tex]\( y = mx + c \)[/tex]
- Substitute the values into the equation:
[tex]\[
y = 0x + (-3)
\][/tex]
- Simplify the equation:
[tex]\[
y = -3
\][/tex]
So, the completed entry for the first part of row d) is:
[tex]\[
\text{d)} \quad m = 0, \quad c = -3, \quad \text{Equation: } y = -3
\][/tex]
4. Row d) [second entry]:
- Given:
- Gradient ([tex]\(m\)[/tex]): -4
- [tex]\(y\)[/tex]-intercept ([tex]\(c\)[/tex]): 0
- Equation form is [tex]\( y = mx + c \)[/tex]
- Substitute the values into the equation:
[tex]\[
y = -4x + 0
\][/tex]
- Simplify the equation:
[tex]\[
y = -4x
\][/tex]
So, the completed entry for the second part of row d) is:
[tex]\[
\text{d)} \quad m = -4, \quad c = 0, \quad \text{Equation: } y = -4x
\][/tex]
### Completed Table:
[tex]\[
\begin{tabular}{|c|c|c|c|}
\hline & \text{Gradient} & y\text{-intercept} & \text{Equation } y = mx + c \\
\hline \text{Example} & m = \frac{1}{2} & c = 4 & y = \frac{1}{2} x + 4 \\
\hline \text{a)} & m = -1 & c = -1 & y = -1x - 1 \\
\hline \text{b)} & m = 0 & c = -6 & y = -6 \\
\hline \text{d) [first entry]} & m = 0 & c = -3 & y = -3 \\
\hline \text{d) [second entry]} & m = -4 & c = 0 & y = -4x \\
\hline
\end{tabular}
\][/tex]
