The graph of y = 2x - 6 crosses the y-axis at what value
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A linear function is a function that forms a straight line when graphed. The general form of a linear function is y equals m x plus b, where m is the slope and b is the y-intercept.
Now let's look at our specific function: y equals 2x minus 6. By comparing this to the general form y equals mx plus b, we can identify that the slope m is 2 and the y-intercept b is negative 6.
The y-intercept is the point where the graph of the function crosses the y-axis. At this point, the value of x is always zero. So for any linear function y equals mx plus b, when x equals zero, y equals b. This means the y-intercept is simply the constant term b.
We can find the y-intercept algebraically by substituting x equals zero into the equation and solving for y. Starting with y equals 2x minus 6, we substitute x equals zero, which gives us y equals 2 times 0 minus 6. Simplifying, we get y equals 0 minus 6, which equals negative 6.
Let's visualize this on a graph. We'll plot the line y equals 2x minus 6. As we can see, the line crosses the y-axis at the point (0, negative 6), which confirms our algebraic calculation.
To verify our answer, we can check that when x equals zero, y equals 2 times 0 minus 6, which equals negative 6. Let's look at a few more examples. For y equals 3x plus 4, the y-intercept is 4. For y equals negative x plus 2, the y-intercept is 2. In each case, the y-intercept is simply the constant term in the equation.