Find the equation of a line in point-slope form given the point (3, 5) and slope m = 6.
Understand the Problem
The question asks to find the equation of a line in point-slope form given a point (3, 5) and slope m = 6. The point-slope form is given by y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.
Answer
$y - 5 = 6(x - 3)$
Answer for screen readers
$y - 5 = 6(x - 3)$
Steps to Solve
- Write down the point-slope form
The point-slope form of a line is given by: $y - y_1 = m(x - x_1)$
- Substitute the given values
We are given the point $(3, 5)$ and the slope $m = 6$. So, $x_1 = 3$, $y_1 = 5$, and $m = 6$. Substitute these values into the point-slope form:
$y - 5 = 6(x - 3)$
$y - 5 = 6(x - 3)$
More Information
The point-slope form is useful because it directly incorporates the slope and a point on the line, making it easy to write the equation when these are known. You can convert this to slope-intercept form ($y = mx + b$) by distributing the 6 and isolating $y$, but the question requires that we leave the answer in point slope form.
Tips
A common mistake is to mix up the $x$ and $y$ coordinates when substituting them into the point-slope form. Also, be careful with signs, especially if the given point has negative coordinates.
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