Use the image to answer the question.
A coordinate plane shows four quadrants with both the x-axis and the y-axis ranging from negative 10 to positive 10 in increments of 2. Two points are plotted and joined by a line. The plotted points are as follows: left parenthesis negative 3 comma 1 right parenthesis, left parenthesis 2 comma negative 4 right parenthesis. A line connects the two plotted points and extends beyond the points in both directions.
Find the slope of the line given its graph.
Responses
−1
negative 1
−5
negative 5
−56
negative Start Fraction 5 over 6 End Fraction
1
The slope of the line can be found using the formula:
\[ \text{slope} = \frac{{\text{change in y-coordinates}}}{{\text{change in x-coordinates}}}\]
Using the given points, the change in y-coordinates is:
\[1 - (-4) = 1 + 4 = 5\]
The change in x-coordinates is:
\[-3 - 2 = -3 - 2 = -5\]
Thus, the slope of the line is: \(\frac{5}{-5}\), which simplifies to \(-1\) or "negative 1".
To find the slope of the line given its graph, we can use the formula for slope:
slope = (change in y)/(change in x)
Let's label the first point as (x₁, y₁) and the second point as (x₂, y₂).
From the graph, we can see that the first point is (-3, 1) and the second point is (2, -4).
Now, we can substitute the coordinates into the formula:
slope = (y₂ - y₁)/(x₂ - x₁)
slope = (-4 - 1)/(2 - (-3))
slope = (-5)/(2 + 3)
slope = (-5)/(5)
slope = -1
Therefore, the slope of the line is -1.
To find the slope of the line given its graph, we can use the formula for slope:
slope = (change in y-coordinates) / (change in x-coordinates)
Looking at the points on the graph, we can see that the first point is (-3, 1) and the second point is (2, -4).
To find the change in y-coordinates, we subtract the y-coordinate of the first point from the y-coordinate of the second point: -4 - 1 = -5.
To find the change in x-coordinates, we subtract the x-coordinate of the first point from the x-coordinate of the second point: 2 - (-3) = 5.
Therefore, the slope of the line is:
slope = (-5) / (5) = -1/1 = -1.
So, the slope of the line is -1.