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What is a point-slope equation of the line with slope −10-10 that goes through the point (1,4)(1,4)?\newline(A) y+4=−10(x+1)y+4=-10(x+1)\newline(B) y−4=−10(x−1)y-4=-10(x-1)\newline(C) y+4=10(x+1)y+4=10(x+1)\newline(D) y−4=10(x−1)y-4=10(x-1)

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Q. What is a point-slope equation of the line with slope −10-10 that goes through the point (1,4)(1,4)?\newline(A) y+4=−10(x+1)y+4=-10(x+1)\newline(B) y−4=−10(x−1)y-4=-10(x-1)\newline(C) y+4=10(x+1)y+4=10(x+1)\newline(D) y−4=10(x−1)y-4=10(x-1)
  1. Point-Slope Form Definition: The point-slope form of a line's equation is given by (y−y1)=m(x−x1)(y - y_1) = m(x - x_1), where mm is the slope and (x1,y1)(x_1, y_1) is a point on the line.
  2. Given Slope and Point: Given the slope m=−10m = -10 and the point (1,4)(1, 4), we can substitute these values into the point-slope form.
  3. Substitute Values: Substituting the values, we get (y−4)=−10(x−1)(y - 4) = -10(x - 1).
  4. Confirm Equation Match: This equation matches one of the given choices, confirming that we have correctly applied the point-slope formula.

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