To find the equation of the linear function, we need to determine the slope and the y-intercept.
Step 1: Determine the slope (m):
The slope of a line passing through two points (x₁, y₁) and (x₂, y₂) is given by the formula:
m = (y₂ - y₁) / (x₂ - x₁)
Using the given points (-1, 4) and (1, 0):
m = (0 - 4) / (1 - (-1))
m = -4 / 2
m = -2
Step 2: Determine the y-intercept (b):
The y-intercept is the value of y when x = 0. One of the given points is (1, 0), which lies on the y-axis. Therefore, the y-intercept is 0.
Step 3: Write the equation using the slope-intercept form:
The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.
Therefore, the equation of the linear function is:
y = -2x + 0
Simplifying, we get:
y = -2x
(-1,4) (1,0) write the equation of the linear function shown on the graph
3 answers
wrong
A. y=2x-2
B. y=-2x+2
C. y=2x+2
D. y=-2x-2
A. y=2x-2
B. y=-2x+2
C. y=2x+2
D. y=-2x-2
Apologies for the mistake. Let's go through the steps again to find the correct equation of the linear function.
Step 1: Determine the slope (m):
The slope of a line passing through two points (x₁, y₁) and (x₂, y₂) is given by the formula:
m = (y₂ - y₁) / (x₂ - x₁)
Using the given points (-1, 4) and (1, 0):
m = (0 - 4) / (1 - (-1))
m = -4 / 2
m = -2
Step 2: Determine the y-intercept (b):
The y-intercept is the value of y when x = 0. One of the given points is (1, 0), which lies on the y-axis. Therefore, the y-intercept is 0.
Step 3: Write the equation using the slope-intercept form:
The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.
Therefore, the equation of the linear function is:
y = -2x + 0
Simplifying, we get:
y = -2x
Apologies for the confusion in my previous response. Based on the given points, the correct equation of the linear function is:
D. y = -2x - 2
Step 1: Determine the slope (m):
The slope of a line passing through two points (x₁, y₁) and (x₂, y₂) is given by the formula:
m = (y₂ - y₁) / (x₂ - x₁)
Using the given points (-1, 4) and (1, 0):
m = (0 - 4) / (1 - (-1))
m = -4 / 2
m = -2
Step 2: Determine the y-intercept (b):
The y-intercept is the value of y when x = 0. One of the given points is (1, 0), which lies on the y-axis. Therefore, the y-intercept is 0.
Step 3: Write the equation using the slope-intercept form:
The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.
Therefore, the equation of the linear function is:
y = -2x + 0
Simplifying, we get:
y = -2x
Apologies for the confusion in my previous response. Based on the given points, the correct equation of the linear function is:
D. y = -2x - 2