1.
Item 1
One linear function is by
f(x)=5x−2
A second linear function g(x) passes through the points (4,0) and (-8,6)
What are the y-intercepts of the two functions?
The y-intercept of f(x) is 5 and the y-intercept of g(x) is 4
The y-intercept of f(x) is 5 and the y-intercept of g(x) is 12
The y-intercept of f(x) is -2 and the y-intercept of g(x) is 2
The y-intercept of f(x) is -2 and the y-intercept of g(x) is 4
I do not need to correct this question.
3 answers
- The correct answer is: The y-intercept of f(x) is -2 and the y-intercept of g(x) is 4
bot gpt 3.5 are you sure
Apologies for the confusion earlier. Let's revisit the calculations for the y-intercepts of the two functions:
For f(x) = 5x - 2:
To find the y-intercept, let x = 0:
f(0) = 5(0) - 2
f(0) = -2
Therefore, the y-intercept of f(x) is -2.
For g(x) passing through the points (4,0) and (-8,6):
Let's find the equation of the line passing through the two points using the slope-intercept form (y = mx + b):
m = (0 - 6) / (4 - (-8)) = -6 / 12 = -1/2
Now, we have the slope (m) and one point (4,0), substitute into the equation to solve for the y-intercept:
0 = (-1/2)(4) + b
0 = -2 + b
b = 2
Therefore, the y-intercept of g(x) is 2.
So, to correct the question: The y-intercept of f(x) is -2 and the y-intercept of g(x) is 2.
For f(x) = 5x - 2:
To find the y-intercept, let x = 0:
f(0) = 5(0) - 2
f(0) = -2
Therefore, the y-intercept of f(x) is -2.
For g(x) passing through the points (4,0) and (-8,6):
Let's find the equation of the line passing through the two points using the slope-intercept form (y = mx + b):
m = (0 - 6) / (4 - (-8)) = -6 / 12 = -1/2
Now, we have the slope (m) and one point (4,0), substitute into the equation to solve for the y-intercept:
0 = (-1/2)(4) + b
0 = -2 + b
b = 2
Therefore, the y-intercept of g(x) is 2.
So, to correct the question: The y-intercept of f(x) is -2 and the y-intercept of g(x) is 2.