Question

what is the slope of the line that passes through the points (4,4) and (10,7)? write your answer in simplest form

Answer 1

`\boxed {\boxed {\sf m= (1)/(2)}}`

Explanation:

We are asked to find the slope of a line that passes through 2 points. The slope tells us the steepness and direction of a line. It is calculated using the following formula:

`m= \frac {y_2-y_1}{x_2-x_1}`

In this formula, (x₁ , y₁) and (x₂, y₂) are the points the line passes through. The points are (4,4) and (10,7). If we match the value and the corresponding variable we see that:

• x₁ = 4
• y₁= 4
• x₂ = 10
• y₂= 7

Substitute the values into the formula.

`m= (7-4)/(10-4)`

Solve the numerator.

• 7-4=3

`m= (3)/(10-4)`

Solve the denominator.

• 10-4= 6

`m= (3)/(6)`

This fraction can be reduced. Both the numerator and denominator can be divided by 3.

`m= (3/3)/(6/3)`

`m= (1)/(2)`

The slope of the line that passes through (4,4) and (10,7) is 1/2.