Answer:
The slope of the line is 4.
Step-by-step explanation:
The equation of a line has the following general format:
[tex]y = ax + b[/tex]
In which a is the slope and b is the y-intercept(the value o y when x = 0).
Line contains the points (2, 6) and (-1, -6).
This means that when [tex]x = 2, y = 6[/tex], and when [tex]x = -1, y = -6[/tex].
We replace both in the general equation and solve the system of equations.
So
[tex]x = 2, y = 6[/tex]
[tex]6 = 2a + b[/tex]
[tex]b = 6 - 2a[/tex]
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[tex]x = -1, y = -6[/tex]
[tex]-6 = -a + b[/tex]
We have b as a function of a in the first equation, so
[tex]-6 = -a + 6 - 2a[/tex]
[tex]3a = 12[/tex]
[tex]a = \frac{12}{3}[/tex]
[tex]a = 4[/tex]
The slope of the line is 4.
