Question What is an equatch Video of the line that passes through the points \( (-6,6) \) and \( (-3,7) \) ?

To find the equation of the line that passes through the points \( (-6, 6) \) and \( (-3, 7) \), we start by calculating the slope (m) using the formula \( m = \frac{y_2 - y_1}{x_2 - x_1} \). Plugging in the points, we get \( m = \frac{7 - 6}{-3 + 6} = \frac{1}{3} \). Now, using the point-slope form \( y - y_1 = m(x - x_1) \) with one of the points (let's use \( (-6, 6) \)), we have \( y - 6 = \frac{1}{3}(x + 6) \). Simplifying this yields the equation of the line as \( y = \frac{1}{3}x + 8 \). Ever wonder how this fits into real life? A line like this can represent various scenarios, like tracking the growth of a plant over time, where one point marks the plant's height at one month and the other point at another month. The slope gives you insight into how quickly that plant is growing! One common mistake when finding the equation of a line is confusing the slope with the y-intercept or mixing up the coordinates. Always double-check which point you’re substituting into the slope-intercept form, and make sure you're subtracting the corresponding y-coordinates and x-coordinates correctly!