A straight line passes through \( (3,8) \) and has a gradient of -7 . The equation of the line is:

To find the equation of the line, you can use the point-slope form of the equation of a line, which is expressed as \( y - y_1 = m(x - x_1) \). Here, \( m \) is the slope (gradient), and \( (x_1, y_1) \) is a point on the line. Plugging in the given values: \( m = -7 \), \( x_1 = 3 \), and \( y_1 = 8 \): \[ y - 8 = -7(x - 3) \] Now, simplify the equation: \[ y - 8 = -7x + 21 \] Adding \( 8 \) to both sides gives: \[ y = -7x + 29 \] So the equation of the line is \( y = -7x + 29 \). Do remember that line equations are like make-believe maps guiding you through a world of coordinates, slopes, and intercepts! Imagine this line zig-zagging through the xy-plane, creating a pathway for your mathematical adventures. Next, practice writing equations with different slopes and points; it's like auditioning for a role in a math play! Your creativity will soar, and you might just discover unique lines to characterize new mathematical stories.