Rewrite the point-slope form of the equation πΊβπ©π€π§=π£π€(πΉβπ§π’) in slope-intercept form. What does the y-intercept represent in terms of the situation? Explain.
To rewrite the equation in slope-intercept form, we need to isolate y on one side of the equation. The given equation is y - 235 = 12(x - 50). We'll distribute the 12 on the right side of the equation:
y - 235 = 12x - 600
Now, let's add 235 to both sides of the equation:
y - 235 + 235 = 12x - 600 + 235
This simplifies to:
y = 12x - 365
The equation is now in slope-intercept form (y = mx + b), where the coefficient of x (m) is the slope of the line, and the constant term (b) is the y-intercept.
In this equation, the slope is 12, meaning that for every unit increase in x, y will increase by 12 units. The y-intercept is -365, which represents the point where the line crosses the y-axis. In terms of the situation, the y-intercept could represent an initial value or a starting point for some variable. For example, if we consider x to represent time, the y-intercept could represent an initial position at time zero.