What is the slope-intercept form of the equation of the line that passes through the point (–6, 1) and is perpendicular to the graph of 2x + 3y = –5?
Answers
Answer:
First, you need to determine the slope of the equation 2x + 3y = -5. To do that, you simply solve for y which would give you y = -2/3x - 5/3. This is in the slope-intercept form, thereby giving you a slope of -2/3.
The slope of lines that are perpendicular to each another will be the negative inverse of each other. The inverse of -2/3 is -3/2, so the slope of the line in question will be the negative of that which equals 3/2.
Now, to determine the slope intercept form, you must start with the point-slope form: y - y1 = m(x - x1). Substituting gives you y - 1 = 3/2 (x - (-6)). Now, solve for y:
y - 1 = 3/2x - (-9)
y - 1 = 3/2x + 9
y = 3/2x + 10
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