Respuesta :
Answer:
The slope of the line that passes through the points (1,7) and (-4,-8) is 3.
Step-by-step explanation:
The equation of a line has the following format.
[tex]y = ax + b[/tex]
In which a is the slope.
Passes through the point (1,7)
When [tex]x = 1, y = 7[/tex]
So
[tex]y = ax + b[/tex]
[tex]7 = a + b[/tex]
Passes through the point (-4, -8)
When [tex]x = -4, y = -8[/tex]
So
[tex]y = ax + b[/tex]
[tex]-8 = -4a + b[/tex]
We have to solve the following system
[tex]a + b = 7[/tex]
[tex]-4a + b = -8[/tex]
We want to find a.
From the first equation
[tex]b = 7 - a[/tex]
Replacing in the second equation
[tex]-4a + b = -8[/tex]
[tex]-4a + 7 - a = -8[/tex]
[tex]-5a = -15[/tex]
[tex]5a = 15[/tex]
[tex]a = \frac{15}{5}[/tex]
[tex]a = 3[/tex]
The slope of the line that passes through the points (1,7) and (-4,-8) is 3.
