A line passes through the point \( (4,-1) \) and has a slope of 2 . Write an equation in slope-intercept form for this line.

To find the equation of the line in slope-intercept form \(y = mx + b\), we start with the slope \(m = 2\) and the point through which the line passes, \( (4, -1) \). We can substitute these values into the equation. First, we can plug in the values to find \(b\): \[ -1 = 2(4) + b \] \[ -1 = 8 + b \] \[ b = -1 - 8 \] \[ b = -9 \] Now that we have the slope and the y-intercept \(b\), we can write the equation: \[ y = 2x - 9 \] Therefore, the equation of the line in slope-intercept form is \(y = 2x - 9\). Now, let's dive into some fun facts! Did you know that the concept of slope can be connected to the steepness of hills? The higher the slope, the steeper the hill, just like climbing a mountain! Also, using slope-intercept form can be super handy in real-world situations, like budgeting! You can represent expenses over time with a straight line and quickly determine your total expenditure at any point. It's like creating your financial roadmap!