A line contains the points (-3, 6) and (2, 1). What is the slope of the line?
The formula for the slope of a line passing through two points (x1, y1) and (x2, y2) is given by:
m = (y2 - y1) / (x2 - x1)
In this case, (x1, y1) = (-3, 6) and (x2, y2) = (2, 1):
m = (1 - 6) / (2 - (-3))
= (-5) / (2 + 3)
= (-5) / 5
= -1
Therefore, the slope of the line is -1.
The equation of a line is
y = - 2x - 4. What is the y-
intercept?
The y-intercept of a line is the point where the line intersects the y-axis. In the equation of a line in the form y = mx + b, the y-intercept is represented by the constant term b.
In this case, the equation of the line is y = -2x - 4. Comparing this equation to the standard form y = mx + b, we can see that the constant term is -4. Therefore, the y-intercept of the line is -4.
The proportional relationship for the earnings and hours worked for Employee 1 is displayed in the table. The proportional relationship between the earnings and hours worked for Employee 2 is displayed in the graph. What is the equation that represents the proportional relationship between the earnings and hours worked for Employee 1 and Employee 2?
To determine the equation that represents the proportional relationship between the earnings and hours worked for Employee 1 and Employee 2, we need to have values for both variables for each employee. Since you have only mentioned that the relationship for Employee 1 is displayed in a table and the relationship for Employee 2 is displayed in a graph, it is not possible to determine the equation without more information.
If you provide the specific values for the earnings and hours worked for both employees, we can use that information to determine the equation representing the proportional relationship between the two.
To find the slope of a line passing through two points, you can use the formula:
slope = (y2 - y1) / (x2 - x1)
Let's plug in the given values:
x1 = -3
y1 = 6
x2 = 2
y2 = 1
slope = (1 - 6) / (2 - (-3))
slope = (-5) / (2 + 3)
slope = -5/5
slope = -1
Therefore, the slope of the line passing through the points (-3, 6) and (2, 1) is -1.
To find the slope of a line, you can use the formula:
m = (y2 - y1) / (x2 - x1)
Where (x1, y1) and (x2, y2) are the coordinates of two points on the line.
In this case, the given points are (-3, 6) and (2, 1).
So, substituting the coordinates into the slope formula, we have:
m = (1 - 6) / (2 - (-3))
= (-5) / (2 + 3)
= (-5) / 5
= -1
Therefore, the slope of the line is -1.