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Find a point on the line and the line's slope. y+4=(1)/(4)(x+5)

Find a point on the line and the line's slope.\newliney+4=14(x+5) y+4=\frac{1}{4}(x+5)

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Full solution

Q. Find a point on the line and the line's slope.\newliney+4=14(x+5) y+4=\frac{1}{4}(x+5)
  1. Rewrite Equation: Rewrite the equation in slope-intercept form y=mx+by = mx + b to identify the slope and a point.y+4=(14)(x+5)y + 4 = \left(\frac{1}{4}\right)(x + 5)y=(14)x+(14)5−4y = \left(\frac{1}{4}\right)x + \left(\frac{1}{4}\right)5 - 4y=(14)x+1.25−4y = \left(\frac{1}{4}\right)x + 1.25 - 4y=(14)x−2.75y = \left(\frac{1}{4}\right)x - 2.75
  2. Identify Slope: Identify the slope from the equation y=(14)x−2.75y = (\frac{1}{4})x - 2.75. The coefficient of xx, which is 14\frac{1}{4}, is the slope.
  3. Find Point: Choose x=0x = 0 to find a corresponding yy-value for a point on the line.\newlineSubstitute x=0x = 0 into y=14x−2.75y = \frac{1}{4}x - 2.75.\newliney=14(0)−2.75y = \frac{1}{4}(0) - 2.75\newliney=−2.75y = -2.75\newlineSo, the point (0,−2.75)(0, -2.75) lies on the line.

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