What is the equation of a line that is perpendicular to y=3x-2 and passes through the point (6,8)?

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.

You are given an equation in the form y=mx+b where m is the slope and b is where the line crosses the y axis, called the y intercept. So slope=3. Any line parallel to that one has the same slope, and any line perpendicular has the negative reciprocal slope, -1/3.

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.

Given the point (6,8):

y - 8 = (-1/3)(x - 6) Point-slope form

y = -x/3 + 10 Slope-intercept form

3y + x - 30 = 0 Standard form, all variables on the left, no fractions, and zero or a constant on the right.