Question

What is the slope of the line that passes through the points (1,7) and (-4,-8)?

Answer 1

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.

$y = ax + b$

In which a is the slope.

Passes through the point (1,7)

When $x = 1, y = 7$

So

$y = ax + b$

$7 = a + b$

Passes through the point (-4, -8)

When $x = -4, y = -8$

So

$y = ax + b$

$-8 = -4a + b$

We have to solve the following system

$a + b = 7$

$-4a + b = -8$

We want to find a.

From the first equation

$b = 7 - a$

Replacing in the second equation

$-4a + b = -8$

$-4a + 7 - a = -8$

$-5a = -15$

$5a = 15$

$a = \frac{15}{5}$

$a = 3$

The slope of the line that passes through the points (1,7) and (-4,-8) is 3.