\( \mid \leftarrow \quad \) Find the slope intercept form of the line whose slope is 2 and that passes through the point \( (-3,7) \).

To find the slope-intercept form of the line, we can use the formula \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept. Given that the slope \( m \) is 2, we can plug in our point \( (-3, 7) \) into the equation: 1. Substitute the values: \( 7 = 2(-3) + b \). 2. This simplifies to \( 7 = -6 + b \). 3. Solving for \( b \) gives us \( b = 13 \). Now we have everything we need! The slope-intercept form of the line is \( y = 2x + 13 \). Isn't it amazing how just a simple formula can express the relationship of a line? You can visualize this line by plotting the point \( (-3, 7) \) and using the slope to find more points. Each step of 2 up for every step of 1 to the right will take you on a straight path that represents all the solutions to the equation! You might be surprised to know that the concept of slope dates back to the works of mathematicians in ancient Greece and later, during the Renaissance, as geometry and algebra blended into precursor forms of calculus! The idea of slope not only helps us plot lines but also leads to understanding rates of change—a foundational concept in physics, economics, and beyond!