Q. A lime has a slope of \( \frac{3}{6} \) and passes through the point \( (-6,6) \). White its equation in slope-intercept fonm. Write your answer using integers, proper firactions, and improper fractions in simplest form.

To find the equation of the line in slope-intercept form, we start with the slope \( \frac{3}{6} \), which simplifies to \( \frac{1}{2} \). Next, we use the point-slope formula \( y - y_1 = m(x - x_1) \), where \( m \) is the slope and \( (x_1, y_1) \) is the point \( (-6, 6) \). Plugging in the values gives us: \[ y - 6 = \frac{1}{2}(x + 6) \] Now, distribute and rearrange: \[ y - 6 = \frac{1}{2}x + 3 \] \[ y = \frac{1}{2}x + 9 \] So, the slope-intercept form of the equation is \( y = \frac{1}{2}x + 9 \). For some added fun: did you know that the concept of slopes dates back to ancient civilizations? The Babylonians were already calculating the slope of angles for their architectural wonders! If you’re ever stuck on determining slopes, remember to double-check whether your fractions are in simplest form. Dividing both the numerator and denominator by their greatest common divisor can save you from slipping into the world of messy equations!