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Write the equation of the line that passes through (4, 2) and is parallel to the line y = 2x – 1.

Sagot :

rspill6

Answer:

Step-by-step explanation:

We will look for a line that has the general form of y = mx + b, where m is the slope and b the y-intercept (the value of y when x = 0).

A line parallel to y=2x-1 will have the same slope, 2.

We can write y = 2x + b for the new line.  We need to find b.  We can use the given point in this equation and solve for b:

y = 2x + b

2 = 2(4) + b  for (4,2)

2 = 8 + b

x = -6

The parallel line to y=2x-1 that goes through point (4,2) is:

y = 2x-6

See the attached graph.

View image rspill6

Hi student, let me help you out! :)

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We are asked to write the equation of the line that passes through (4, 2) and is parallel to y=2x-1.

[tex]\triangle~\fbox{\bf{KEY:}}[/tex]

  • Parallel lines have the same slope.

Since the slope of the given line is 2, the slope of the line parallel to this one is also 2.

Now, figure out the y-intercept, c:

y=2x+c

We're given a point: (4, 2).

Where: 2 is the y-coordinate of the point, and 4 is the x-coordinate.

Now, substitute 2 for y and 4 for x:

[tex]\longmapsto\sf{2=2(4)+c}[/tex]

Simplify!

[tex]\longmapsto\sf{2=8+c}[/tex]

Subtract 8 from both sides of the equal sign:

[tex]\longmapsto\sf{2-8=c}[/tex]

[tex]\longmapsto\sf{-6=c}[/tex]

Hope it helps you out! :D

Ask in comments if any queries arise.

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