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Find the line's slope and a point on the line. y+1=(2)/(3)(x-1)

Find the line's slope and a point on the line.\newliney+1=23(x−1) y+1=\frac{2}{3}(x-1)

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Full solution

Q. Find the line's slope and a point on the line.\newliney+1=23(x−1) y+1=\frac{2}{3}(x-1)
  1. Rewrite Equation: Rewrite the equation in slope-intercept form y=mx+by = mx + b to identify the slope and y-intercept.\newliney+1=(23)(x−1)y + 1 = \left(\frac{2}{3}\right)(x - 1)\newliney=(23)x−(23)−1y = \left(\frac{2}{3}\right)x - \left(\frac{2}{3}\right) - 1\newliney=(23)x−(23)−(33)y = \left(\frac{2}{3}\right)x - \left(\frac{2}{3}\right) - \left(\frac{3}{3}\right)\newliney=(23)x−(53)y = \left(\frac{2}{3}\right)x - \left(\frac{5}{3}\right)
  2. Identify Slope: Identify the slope mm from the equation y=23x−53y = \frac{2}{3}x - \frac{5}{3}.\newlineSlope, m=23m = \frac{2}{3}
  3. Find Point on Line: Identify a point on the line using the y-intercept found in the equation.\newlineThe y-intercept is at y=−53y = -\frac{5}{3}, which corresponds to the point (0,−53)(0, -\frac{5}{3}) on the y-axis.

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