To find the equation of a line given a point and the slope, we use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept.
1. We're given the point (7,7) and the slope m = -7.
2. We know that the slope m = -7, and we have a point (x, y) = (7, 7).
3. We substitute these values into the equation y = mx + b to solve for b, the y-intercept. Substituting these values gives
7 = -7(7) + b.
4. Solving this equation for b, we have
b = 7 + 7*7 = 56
So, the equation of the line in slope-intercept form is y = -7x + 56.
But, since the slope is negative, we have to invert the sign.
In conclusion, the equation of the line is y = 7x + 56.