Question

find the slope of the line passing through the pair of points or state that the slope is undefined. then indicate whether the line through the point rises , falls is horizontalor is vertical (4.1) and (10.6)

Answer 1

The points given are:

(4, 1) and (10, 6)

We can find the slope using the formula below:

$\text{slope}=\frac{y_2-y_1}{x_2-x_1}$

From the points given;

x₁=4 y₁=1 x₂ =10 y₂=6

substitute the values into the formula

$\text{slope}=\frac{6-1}{10-4}$$=\frac{5}{6}$

To find whether the line rises or falls or is horizontal, let's find the equation of the line

substitute x₁=4 y₁=1 and m=5/6 into y=mx + b and find the intercept(b)

1=5/6 (4) + b

1= 10/3 + b

1-10/3 = b

-7/3 = b

substitute m=5/6 and b=-7/3 into y=mx + b, this gives the equation of the line.

That is;

$y=\frac{5}{6}x-\frac{7}{3}$

From, this, since the slope is positive, then the line rises