Find an equation of the line passing through the pair of points. \( (4,-1),(-20,17) \) Sketch the line.

To find the equation of the line passing through the points (4, -1) and (-20, 17), we can start by calculating the slope (m) using the slope formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{17 - (-1)}{-20 - 4} = \frac{18}{-24} = -\frac{3}{4} \] Now, we can use the slope-intercept form of the line equation, \(y = mx + b\). To find b (the y-intercept), we can substitute one of the points into the equation. We'll use the point (4, -1): \[ -1 = -\frac{3}{4}(4) + b \Rightarrow -1 = -3 + b \Rightarrow b = 2 \] Thus, the equation of the line is: \[ y = -\frac{3}{4}x + 2 \] To sketch the line, you can plot the two given points (4, -1) and (-20, 17), then draw a straight line through them. Make sure your line has a downward slope consistent with the negative value of the slope! Plot points (4, -1) and (-20, 17) on a coordinate plane, and draw a line connecting them. The line will slope downwards from left to right, reflecting the negative slope.