A line is graphed on a coordinate grid through the points with coordinates
negative 1 comma 4, coordinates 0 comma 2, coordinates 1 comma 0, coordinates 2 comma negative 2.
A. one-half
B. 2
C. –2
D. –one-half
First, we need to find the slope of the line. The slope of a line passing through two points (x1,y1) and (x2,y2) is given by the formula (y2-y1)/(x2-x1). Therefore,
slope = (2-4)/(0-(-1)) = 2
Next, since we have the y-intercept of the line (0,2), we can write the equation of the line in slope-intercept form: y = 2x + 2
Now, we just need to find the slope of a line perpendicular to this line. The slopes of perpendicular lines are negative reciprocals of each other. Therefore, the slope of the line perpendicular to our given line is -1/2.
Hence, the answer is D) -one-half.
To find the equation of the line, we need to find the slope of the line using the given points.
The formula for finding the slope of a line passing through two given points (x₁, y₁) and (x₂, y₂) is:
slope = (y₂ - y₁) / (x₂ - x₁)
Let's calculate the slope using the given points:
- Point 1: (-1, 4)
- Point 2: (0, 2)
slope = (2 - 4) / (0 - (-1))
= -2 / (0 + 1)
= -2 / 1
= -2
The slope of the line is -2.
Now, we can use the point-slope form of a linear equation to find the equation of the line.
The point-slope form of a linear equation is:
y - y₁ = m(x - x₁)
Using point 1 (-1, 4) and the slope -2, we can substitute the values into the equation:
y - 4 = -2(x - (-1))
y - 4 = -2(x + 1)
Now, we can simplify the equation:
y - 4 = -2x - 2
y = -2x - 2 + 4
y = -2x + 2
So, the equation of the line passing through the given points is y = -2x + 2.
Looking at the answer choices, we can see that the slope of the line is -2, which matches option C. Therefore, the correct answer is option C, -2.
To find the slope of the line, we use the formula: slope = (change in y)/(change in x).
Let's calculate the changes in y and x for each set of coordinates:
Change in y for the first set of coordinates = 4 - 2 = 2
Change in x for the first set of coordinates = -1 - 0 = -1
Change in y for the second set of coordinates = 2 - 0 = 2
Change in x for the second set of coordinates = 0 - (-1) = 1
Change in y for the third set of coordinates = 0 - 2 = -2
Change in x for the third set of coordinates = 1 - 0 = 1
Change in y for the fourth set of coordinates = -2 - 0 = -2
Change in x for the fourth set of coordinates = 2 - 1 = 1
Now, let's calculate the slope:
Slope = (change in y)/(change in x)
Slope = (2)/(-1) = -2
Therefore, the slope of the line is -2.
The correct answer is C. –2.