Write the point-slope form of the equation of the line that passes through the points (6, -9) and (7, 1). Include your work in your final answer. Type your answer in the box provided to submit your solution.
Question
Write the point-slope form of the equation of the line that passes through the points (6, -9) and (7, 1). Include your work in your final answer. Type your answer in the box provided to submit your solution.
Solution
The point-slope form of a linear equation is given by the formula:
y - y1 = m(x - x1)
where m is the slope of the line and (x1, y1) is a point on the line.
First, we need to find the slope (m) of the line passing through the points (6, -9) and (7, 1). The formula to find the slope between two points (x1, y1) and (x2, y2) is:
m = (y2 - y1) / (x2 - x1)
Substituting the given points into the formula, we get:
m = (1 - (-9)) / (7 - 6) = 10
Now, we can substitute m = 10 and one of the points, say (6, -9), into the point-slope form equation. This gives us:
y - (-9) = 10(x - 6)
Simplifying this equation gives us the final answer:
y + 9 = 10x - 60
So, the point-slope form of the equation of the line that passes through the points (6, -9) and (7, 1) is y + 9 = 10x - 60.
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