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Novay_Z [31]
2 years ago
9

Write an equation of a line in slope-intercept form that passes through (-3,5) and is parallel to y = -6x +1.

Mathematics
1 answer:
katrin2010 [14]2 years ago
4 0

Answer:

a) The equation of the Parallel line to the given straight line is

       6 x + y + 13 =0

b) Slope - intercept form

        y = - 6 x - 13

c) The intercept - form

            \frac{x}{\frac{-13}{6} } + \frac{y}{-13} = 1

x - intercept  =  \frac{-13}{6}

y - intercept = - 13

Step-by-step explanation:

<u><em>Step(i):-</em></u>

Given the equation of the straight line

                             y = -6x +1

                  6 x + y - 1 = 0

The equation of the Parallel line to the given straight line is

                6x + y + k=0 and it passes through the point (-3, 5 )

           ⇒ 6 (-3 ) + 5 + k =0

          ⇒  - 18 + 5 + k=0

         ⇒   -13 + k = 0

        ⇒     k = 13

The equation of the Parallel line to the given straight line is

       6 x + y + 13 =0

<u><em>Step(ii):-</em></u>

Slope - intercept form

                y = m x + C

                y = - 6 x - 13

<u><em>Step(iii)</em></u>:-

Intercept - form

              6 x + y + 13 =0

              6 x + y = - 13

              \frac{6x + y}{-13} = \frac{-13}{-13}

             \frac{6x}{-13} + \frac{y}{-13} = 1

             \frac{x}{\frac{-13}{6} } + \frac{y}{-13} = 1

The intercept - form

            \frac{x}{\frac{-13}{6} } + \frac{y}{-13} = 1

x - intercept  =  \frac{-13}{6}

y - intercept = - 13

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