Cartos is drawing Eू trend line on his scatter plot His line goes through the points \( (10,3) \) and \( (7,9) \) Which is the equation of his line? \( y=-\frac{1}{2} x-\frac{20}{3} \) \( y=\frac{1}{2} x-\frac{20}{3} \) \( y=-2 x-5 \) \( y=-2 x+23 \)

To find the equation of the line that passes through the points \( (10,3) \) and \( (7,9) \), we first need to calculate the slope (m). Using the formula \( m = \frac{y_2 - y_1}{x_2 - x_1} \), we plug in our coordinates: \( m = \frac{9 - 3}{7 - 10} = \frac{6}{-3} = -2 \). Now we can use the slope-intercept form \( y = mx + b \). With \( m = -2 \) and using the point \( (10,3) \), we solve for \( b \): \( 3 = -2(10) + b \) ➜ \( b = 20 + 3 = 23 \). Thus, the equation is \( y = -2x + 23 \). This line not only connects two points on a graph, but it also indicates a specific relationship between the variables, showcasing how one can decrease as the other increases. In real-world scenarios, trend lines help visualize correlations, trends, or patterns, such as analyzing sales over time or studying temperature changes over months while allowing analysts to make informed predictions and decisions.