Question

v. graph each of the inequalities:

1. $3x + 2y \leq 4$
2. $y < x$
3. find the distance between the following pair of points:

$(2,1), (10,7)$

1. graph the line determined by the two points, and find the slope of the line:

$(3,1), (-2, -2)$

1. graph the line that passes through the given point and has the given slope:

$(-1,0) \quad m = \frac{3}{4}$

Explanation:

Step1: Recall the distance formula

The distance \( d \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \( d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2} \).

Step2: Identify the coordinates

For the points \((2,1)\) and \((10,7)\), we have \( x_1 = 2,y_1 = 1,x_2=10,y_2 = 7 \).

Step3: Substitute into the formula

First, calculate \( x_2 - x_1=10 - 2 = 8 \) and \( y_2 - y_1=7 - 1 = 6 \).
Then, \( d=\sqrt{8^2+6^2}=\sqrt{64 + 36}=\sqrt{100} \).

Step4: Simplify the square root

Since \( \sqrt{100}=10 \), the distance between the two points is 10.

Answer:

10