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Answer:
y - 1 = 3/2(x - 6)
Step-by-step explanation:
First, we need to find the slope of the given equation. Without a graph, the easiest way to do this is by isolating y.
2x + 3y = 18
3y = -2x + 18 (Subtract 2x from both sides)
y = -2/3x + 6 (Divide both sides by 3)
The slope is -2/3. Perpendicular lines have opposite reciprocal slopes, so a line perpendicular to this one would need to have a slope of 3/2. We're given a point for this line, so we can write the equation for it in point-slope form.
Point-Slope Form:
y - 1 = 3/2(x - 6)
If necessary, this can also be written in slope-intercept form by solving for y.