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Use point-slope form to write the equation of a line that passes through the point (-1,-4) with slope (7)/(4). Answer:

Use point-slope form to write the equation of a line that passes through the point (−1,−4) (-1,-4) with slope 74 \frac{7}{4} .\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,−4) (-1,-4) with slope 74 \frac{7}{4} .\newlineAnswer:
  1. Identify Point-Slope Form: Identify the point-slope form of a linear equation.\newlineThe point-slope form of a linear 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. Plug Values: Plug the given point and slope into the point-slope form.\newlineGiven point (x1,y1)(x_1, y_1): (−1,−4)(-1, -4)\newlineGiven slope (m)(m): 74\frac{7}{4}\newlineSubstitute these values into the point-slope form equation: (y−(−4))=(74)(x−(−1))(y - (-4)) = \left(\frac{7}{4}\right)(x - (-1))
  3. Simplify Equation: Simplify the equation.\newlineSimplify the equation by removing the parentheses and rewriting the equation as: y+4=(74)(x+1)y + 4 = \left(\frac{7}{4}\right)(x + 1)
  4. Distribute Slope: Distribute the slope to the terms inside the parentheses.\newlineMultiply 74\frac{7}{4} by each term inside the parentheses: y+4=(74)x+(74)(1)y + 4 = \left(\frac{7}{4}\right)x + \left(\frac{7}{4}\right)(1)
  5. Simplify Constant Term: Simplify the constant term.\newlineMultiply 74\frac{7}{4} by 11 to get 74\frac{7}{4}: y+4=(74)x+74y + 4 = \left(\frac{7}{4}\right)x + \frac{7}{4}
  6. Write Final Equation: Write the final equation in point-slope form.\newlineThe final equation of the line in point-slope form is: y+4=(74)x+74y + 4 = \left(\frac{7}{4}\right)x + \frac{7}{4}

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