Question
The graph of a linear function, `f`, is shown. What is the y-intercept of the line?
plotted points are 4,0 and 2, 0
plotted points are 4,0 and 2, 0
Answers
GPT-4o mini
The points provided, (4, 0) and (2, 0), indicate that both points lie on the x-axis, making the graph a horizontal line along the x-axis. In this case, the function does not have a y-intercept since it does not cross the y-axis.
For any linear function in the form \( f(x) = mx + b \) where \( m \) is the slope and \( b \) is the y-intercept, a horizontal line would have a slope of 0 (indicating no rise as x changes), resulting in the equation \( f(x) = 0 \). The line does not cross the y-axis, and thus has no y-intercept in the traditional sense.
Therefore, the answer is that the line does not have a y-intercept.
For any linear function in the form \( f(x) = mx + b \) where \( m \) is the slope and \( b \) is the y-intercept, a horizontal line would have a slope of 0 (indicating no rise as x changes), resulting in the equation \( f(x) = 0 \). The line does not cross the y-axis, and thus has no y-intercept in the traditional sense.
Therefore, the answer is that the line does not have a y-intercept.