Problem: write the equation of the line (in slope-intercept form) passing through (4,6) and?

Slope is rise over run. Run is horizontal distance, left to right. Run is always positive because we always go left to right. Rise is the vertical change in that same distance. A negative rise means it drops. Your example runs 4 units from 0 to 4 and rises -9 units from 17 to 6. Slope m = -9/4

The equation of a line is y = mx where m is the slope. That line passes through the origin. If you want it to pass through some point (a, b) you subtract the coordinates like this: y - b = m(x - a). That is the point-slope form, and you can rewrite it in other forms if it is convenient. You may do this with any point on the line. They all reduce to the same equation.

y - 17 = (-9/4)x This is point-slope form. Notice that we use parentheses to avoid misunderstanding. We could also write y - 17 = -9x/4

y = -9x/4 + 17 This is slope-intercept form.

y + 9x/4 - 17 = 0 This is standard form, all variables on the left, no fractions, and 0 or a constant on the right.