Calculate the point-slope form of the equation of a line passing through the point (4,7) with a slope of −1.*5 pointsy-7 = -x+4y+7 = -x+4y-7 = x-4y+7 = -x-4
Question
Calculate the point-slope form of the equation of a line passing through the point (4,7) with a slope of −1.*5 pointsy-7 = -x+4y+7 = -x+4y-7 = x-4y+7 = -x-4
Solution
The point-slope form of the equation of a line is given by y - y1 = m(x - x1), where m is the slope of the line and (x1, y1) is a point on the line.
Given that the line passes through the point (4,7) and has a slope of -1, we can substitute these values into the equation to get:
y - 7 = -1(x - 4)
Simplify the equation to get:
y - 7 = -x + 4
Add 7 to both sides to isolate y:
y = -x + 4 + 7
So, the point-slope form of the equation of the line is:
y = -x + 11
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