 To write an equation for a line, we need a point hk on the line and the slope m of the line. If we have these, we can write the point-slope equation of the line y equals mx minus h plus k. We can get this information from the graph, provided we can read the graph accurately enough. A useful idea to remember if possible, find points at the intersection of grid lines. For example, let's try to write the equation for the line shown. So again, if possible, we'll find points at the intersection of grid lines, and so we find, and so our graph goes through the point 2, 3, and it also goes through the point 5, 5. Now, given the two points we have a formula that we can use to calculate the slope, but it's probably just as easy to remember that the slope of a line between the two points is rise over run. So to go between the two points, we have to go over three units, then up two units. And so the slope, rise over run, is two-thirds, and so an equation for the line is, and at this point we can do anything at all once we have the equation of a line. So let's find the equation for a line parallel to the given line that passes through the point 5, 0. So remember parallel lines have the same slope, and this line has slope two-thirds. So the line we want passes through 5, 0 with slope two-thirds. So an equation would be, or we could even find the equation for a line perpendicular. So remember these slopes of perpendicular lines are negative reciprocals. So the line shown has slope two-thirds. So a perpendicular line would have slope negative 1 divided by two-thirds, which would be, and so an equation for the line passing through 2, 3, with slope negative 3-halves is...