A line passes through the origin and through the point \( (-3,4) \). What is the slope of the line? a. \( -\frac{4}{3} \) b. \( -\frac{3}{4} \) c. \( \frac{4}{3} \) d. \( \frac{3}{4} \) e. \( \frac{1}{3} \) Whirh of to

To find the slope of a line that passes through the origin (0,0) and the point (-3, 4), we use the formula for slope \( m = \frac{y_2 - y_1}{x_2 - x_1} \). Here, we can take \( (x_1, y_1) \) as (0, 0) and \( (x_2, y_2) \) as (-3, 4). Plugging in the values, we get \( m = \frac{4 - 0}{-3 - 0} = \frac{4}{-3} = -\frac{4}{3} \). So the correct answer is a. \( -\frac{4}{3} \). But wait! Did you know that the concept of slope is like the steepness of a hill? Positive slopes go uphill (like climbing a mountain), while negative slopes mean you're going downhill (like sliding down a slope)! One common mistake when calculating slope is forgetting to subtract the coordinates in the correct order. Always remember to use \( (y_2 - y_1) \) over \( (x_2 - x_1) \) to get it right. Taking the wrong order can flip your slope sign, leading to confusion!