The graph of y = 3x - 3 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 the x-coordinate is zero. In the equation y equals m x plus b, the y-intercept is simply the constant term b.
Now let's analyze our specific equation: y equals 3 x minus 3. Comparing this to the general form y equals m x plus b, we can identify that the slope m equals 3 and the y-intercept b equals negative 3.
To find where the line crosses the y-axis, we substitute x equals zero into the equation. Starting with y equals 3 x minus 3, we replace x with 0, giving us y equals 3 times 0 minus 3. This simplifies to y equals 0 minus 3, which equals negative 3.
Let's graph the equation y equals 3 x minus 3 to visually confirm our result. We'll plot several points: when x is negative 1, y is negative 6; when x is 0, y is negative 3; when x is 1, y is 0; and when x is 2, y is 3. Connecting these points creates our line, and we can clearly see it crosses the y-axis at negative 3.
In conclusion, we've determined that the graph of y equals 3 x minus 3 crosses the y-axis at y equals negative 3. We confirmed this using both the algebraic method, where we substituted x equals zero into the equation, and the direct identification method, where we recognized that the constant term negative 3 is the y-intercept.