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Use point-slope form to write the equation of a line that passes through the point (1,-19) with slope (7)/(5). Answer:

Use point-slope form to write the equation of a line that passes through the point (1,−19) (1,-19) with slope 75 \frac{7}{5} .\newlineAnswer:

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Full solution

Q. Use point-slope form to write the equation of a line that passes through the point (1,−19) (1,-19) with slope 75 \frac{7}{5} .\newlineAnswer:
  1. Recall Point-Slope Form: Recall the point-slope form of a line's equation. 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. Identify Slope and Point: Identify the slope (mm) and the point (x1,y1x_1, y_1) through which the line passes.\newlineSlope (mm): 75\frac{7}{5}\newlinePoint (x1,y1x_1, y_1): (1,−19)(1, -19)
  3. Substitute into Equation: Substitute the slope and point into the point-slope form equation.\newlineUsing the point-slope form, we substitute m=75m = \frac{7}{5}, x1=1x_1 = 1, and y1=−19y_1 = -19 into the equation:\newliney−(−19)=(75)(x−1)y - (-19) = \left(\frac{7}{5}\right)(x - 1)
  4. Simplify Equation: Simplify the equation. y+19=(75)(x−1)y + 19 = \left(\frac{7}{5}\right)(x - 1) This is the equation of the line in point-slope form.

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