Given two points (x₁, y₁) and (x₂, y₂), the slope of the line that passes through these two points can be calculated using the formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}\ldots(1)[/tex]
Using an arbitrary point of the line (x₀, y₀), the slope-point form of the line equation is:
[tex]y-y_0=m(x-x_0)\ldots(2)[/tex]
Now, from the problem:
(a)
[tex]\begin{gathered} (x_1,y_1)=(1,9) \\ (x_2,y_2)=(3,9) \end{gathered}[/tex]
Using (1) to find the slope of the line:
[tex]\begin{gathered} m=\frac{9-9}{3-1} \\ \Rightarrow m=0 \end{gathered}[/tex]
Now, using (1, 9) and (2):
[tex]\begin{gathered} y-9=0(x-1) \\ \Rightarrow y=9 \end{gathered}[/tex]
The equation of the line is y = 9
(c)
[tex]\begin{gathered} (x_1,y_1)=(4.2,7.6) \\ (x_2,y_2)=(-1.6,9.1) \end{gathered}[/tex]
Using (1) to find the slope of the line:
[tex]m=\frac{9.1-7.6}{-1.6-4.2}=\frac{1.5}{-5.8}=-\frac{15}{58}[/tex]
Now, using (4.2, 7.6) and (2):
[tex]y-7.6=-\frac{15}{58}(x-4.2)[/tex]
Rounding to two decimal places:
[tex]y=-0.26x+8.69[/tex]
