The graph of y = 4x - 4 crosses the y-axis at what value
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Linear equations create straight lines when graphed. The general form is y equals m x plus b, where m represents the slope of the line and b represents the y-intercept.
The y-intercept is the point where a line crosses the y-axis. This occurs when x equals zero. At this point, the coordinates are zero comma b, where b is the y-intercept value.
Let's examine our specific equation: y equals four x minus four. Comparing this with the general form y equals m x plus b, we can identify that the slope m equals four and the y-intercept b equals negative four.
To find where the line crosses the y-axis, we substitute x equals zero into the equation. y equals four times zero minus four. This simplifies to y equals zero minus four, which equals negative four. Therefore, the line crosses the y-axis at y equals negative four.
Let's graph the complete equation to verify our result. The line y equals four x minus four passes through the point (zero, negative four) on the y-axis. We can also see other points on the line, such as (one, zero) and (zero point five, negative two), which confirm the slope of four.
To summarize our solution, we used two methods to find the y-intercept. Method one was direct identification from the equation form, where we saw that b equals negative four. Method two was substitution, where we substituted x equals zero into the equation to get y equals negative four. Both methods confirm that the graph of y equals four x minus four crosses the y-axis at y equals negative four.