The graph of y = 4x - 5 crosses the y-axis at what value
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Linear equations are mathematical expressions that form 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. In our specific case, the equation is y equals 4x minus 5, which means the slope is 4 and the y-intercept is negative 5.
The y-intercept is the point where a line crosses the y-axis. At this point, the x-coordinate is always zero. So to find the y-intercept, we substitute x equals zero into our equation. For any linear equation in the form y equals m x plus b, when x is zero, y equals b. This means the y-intercept is the constant term b in the equation.
To find the y-intercept algebraically, we substitute x equals zero into our equation. Starting with y equals 4x minus 5, we replace x with zero. This gives us y equals 4 times 0 minus 5. Simplifying, we get y equals 0 minus 5, which equals negative 5. Therefore, the y-intercept is negative 5, and the line crosses the y-axis at the point (0, negative 5).
Let's verify our result by plotting the line. We'll calculate several points on the line by substituting different x-values into our equation. When x is negative 2, y is negative 13. When x is negative 1, y is negative 9. When x is 0, y is negative 5. When x is 1, y is negative 1. And when x is 2, y is 3. Plotting these points and connecting them forms our line. As we can see, the line clearly crosses the y-axis at the point (0, negative 5), confirming our algebraic calculation.
To summarize our findings: The graph of y equals 4x minus 5 crosses the y-axis at the value y equals negative 5. This occurs at the point (0, negative 5). This value comes directly from the constant term in our linear equation. In any linear equation of the form y equals m x plus b, the y-intercept is always the b value. Understanding this relationship helps us quickly identify key characteristics of linear functions just by looking at their equations.