Question

What is the slope of this line?

2

12

−12

−2
The figure shows a graph of a line in a coordinate plane. The line slants down and to the right passing through the points begin ordered pair negative 3 comma 3 end ordered pair and begin ordered pair 1 comma negative 5 end ordered pair.

Answer 1

The slope of the line passing through the points (-3, 3) and (1, -5) is -2.

Step-by-step explanation:

To calculate the slope of a line passing through two points, you can use the formula: Slope (m) = (change in y) / (change in x). In this case, the coordinates (-3, 3) and (1, -5) give us two points on the line.

The change in y is -5 - 3 = -8, and the change in x is 1 - (-3) = 4. Therefore, the slope is -8 / 4 = -2.

Now, let's understand the geometric interpretation of the slope. A slope of -2 means that for every unit increase in the x-direction, the corresponding y-value decreases by 2 units. It indicates the steepness and direction of the line on the coordinate plane. In this specific line, as x increases, y decreases at a rate of 2:1.

In summary, the slope of -2 defines the rate at which the line descends as it moves to the right. This information helps to understand the relationship between the x and y coordinates on the graph and the inclination of the line in the given coordinate plane.

Answer 2

Slope = -2

Step-by-step explanation:

Given:

The points on the line are given as:

`(x_1,y_1)=(-3,3)\\\\(x_2,y_2)=(1,-5)`

The slope of a line passing through points is given as:

`m=(y_2-y_1)/(x_2-x_1)`

Plug in the given values and solve for slope, 'm'. This gives,

`m=(-5-3)/(1-(-3))\\\\m=(-8)/(1+3)\\\\m=(-8)/(4)\\\\m=-2`

Therefore, the slope of the line given in the graph is -2. So, the last option is correct.