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Write the standard form equation of the line that passes through the point p and is parallel to the line l. p : (-1, 0) l : y = (8/3)x – (17/3) Write the standard form equation of the line passing through these two points. p1 : (0, -3) p2 : (3, -5) Graph the following equation

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Write the standard form equation of the line that passes through the point p and is parallel to the line l.
p : (-1, 0)
l : y = (8/3)x – (17/3)

Write the standard form equation of the line passing through these two points.
p1 : (0, -3)
p2 : (3, -5)

Graph the following equation.




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    1 Answer

    1. Quizzma Team

      Let’s break down your questions step by step.

      ### 1. Standard Form Equation of the Line Parallel to Line l

      First, we need to find the slope of the given line l, which is in slope-intercept form:

      ( y = frac{8}{3}x – frac{17}{3} )

      Here, the slope (m) is ( frac{8}{3} ). Since parallel lines have the same slope, the slope of the line we need to find is also ( frac{8}{3} ).

      Next, we can use the point-slope form of the equation of a line, which is:

      ( y – y_1 = m(x – x_1) )

      Where ( (x_1, y_1) ) is the point p (-1, 0).

      Substituting in the values:

      ( y – 0 = frac{8}{3}(x + 1) )

      ( y = frac{8}{3}x + frac{8}{3} )

      To convert it to standard form ( Ax + By = C ), we will clear the fraction:

      Multiply everything by 3:

      ( 3y = 8x + 8 )

      Rearranging gives:

      ( -8x + 3y = 8 )

      Multiplying through by -1, we get:

    3. Quizzma Team

      Let’s tackle your questions one by one.

      1. Write the standard form equation of the line that passes through the point p and is parallel to the line l.

      First, let’s identify the slope of the given line l, which is in slope-intercept form ( y = mx + b ). Here, the slope ( m ) is ( frac{8}{3} ).

      Since the line we want is parallel, it will have the same slope. So, the slope of our desired line is also ( frac{8}{3} ).

      Using the point-slope form of a line’s equation, which is ( y – y_1 = m(x – x_1) ), we can substitute ( p(-1, 0) ) into the equation:

      [

      y – 0 = frac{8}{3}(x + 1)

      ]

      Expanding this gives:

      [

      y = frac{8}{3}x + frac{8}{3}

      ]

      To convert this to standard form ( Ax + By = C ), we rearrange:

      [

      -frac{8}{3}x + y = frac{8}{3}

      ]

      Multiply through by 3 to eliminate the fraction:

      [

      -8x + 3y = 8

      ]

      We can multiply the entire equation by -1 to get:

      [

      8x – 3y = -8

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