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A line is perpendicular to y = −1/3x + 7

and intersects the point (4,2).
What is the equation of this
perpendicular line?
y = [?]x + [ ]
Hint: Use the Point-Slope Form: y - y₁ = m(x - X1)
Then write the equation in slope-intercept form.

1 Answer

5 votes

A line that is perpendicular to the line y = -1/3x + 7 has a slope that is the negative reciprocal of -1/3 which is 3.

We know that the line intersects the point (4,2), so we can use this point and the slope to write the equation of the line in point-slope form:

y - y1 = m(x - x1)

where (x1, y1) is the point the line passes through, m is the slope, and y and x are the coordinates of any point on the line.

So the equation of the line that is perpendicular to y = −1/3x + 7 and intersects the point (4,2) is:

y - 2 = 3(x - 4)

Simplifying this, we get

y = 3x - 2

To convert this to the slope-intercept form we can rewrite it as

y = 3x + b

Therefore, the equation of the line that is perpendicular to y = −1/3x + 7 and intersects the point (4,2) is y = 3x - 2

User Shane Doyle
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