Respuesta :

MrGumby

Answer:

The parallel equation is y = 0.8x + 6.8

Step-by-step explanation:

In order to find the equation of any line, we first start with the slope. The slope will be the same as the original equation (0.8) since parallel lines share slope. Then we can use slope intercept form and a point to find the intercept.

y = mx + b

6 = 0.8(-1) + b

6 = -0.8 + b

6.8 = b

This allows us to model the equation as y = 0.8x + 6.8

akposevictor

The equation of the line that is parallel to  [tex]y = 0.8x - 3[/tex] and passes through (-1, 6) is:

[tex]\mathbf{y = 0.8x + 6.8}[/tex]

Recall:

  • Parallel lines have the same slope value
  • Slope-intercept equation is: [tex]y = mx + b[/tex]
  • m = slope; b = y-intercept

Given that a line is parallel to [tex]y = 0.8x - 3[/tex], since the slope (m) of [tex]y = 0.8x - 3[/tex] is 0.8, therefore:

  • the slope (m) of the parallel line is: 0.8

Let's Find the y-intercept (b) of the parallel line that also passes through the point, (-1, 6):

  • Substitute (x, y) = (-1, 6) and m = 0.8 into [tex]y = mx + b[/tex] to find b

  • Thus:

[tex]6 = 0.8(-1) + b\\\\6 = -0.8 + b\\\\6 + 0.8 = b\\\\6.8 = b\\\\b = 6.8[/tex]

Write the equation by substituting b = 6.8 and m = 0.8 into  [tex]y = mx + b[/tex]:

  • Thus:

[tex]y = 0.8x + 6.8[/tex]

Therefore, the equation of the line that is parallel to  [tex]y = 0.8x - 3[/tex] and passes through (-1, 6) is:

[tex]\mathbf{y = 0.8x + 6.8}[/tex]

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https://brainly.com/question/2564656

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