Passestrough (2,4) and perpendicular to 4x-2y=14

Answer 1

4x = 2y+14

4x-14 = 2y

2x-7 = y

the slope of the given line is 2

the slope of the perpendicular line is -1/2

B = y - mx

= 4 - (-1/2)(2)

= 4 + 1

= 5

y = (-1/2)x + 5

Answer 2

Write the equation that Passes through (2,4) and perpendicular to 4x-2y=14

We can simplify the line into the slope intercept form like so.....

4x-2y=14.........add 2y to both sides of the equal sign to get......

4x = 2y + 14......subtract 14 from both sides to get....

2y = 4x-14..........divide both sides by 2 to get the final slope intercept form......

y = 2x - 7 ............this is the slope intercept form....y = mx + b....where m = slope

Write the equation that Passes through (2,4) and perpendicular to 4x-2y=14

You want to research and verify the following 2 principles related to perpendicular lines.

The slopes of two perpendicular lines are negative reciprocals.

The product of the slopes of two perpendicular lines is -1 since

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Write the equation that Passes through (2,4) and perpendicular to 4x-2y=14

We need the slope.....or the m portion of the equation so for the line....rewritten we have...

y = 2x - 7.....the slope is m = 2....Right?

Now using the given principles a line perpendicular to this one has a slope that is the negative reciprocal...hmmm

.....let's see....the reciprocal is 1/x....so the reciprocal in this case 1/2......but we are not done yet...

...the slope for a perpendicular line is "negative reciprocal".....so -1/2 is the slope of 2nd line....

....verify.....2 * -1/2 = -1.......that verifies the 2nd principle above.......

Write the equation that Passes through (2,4) and perpendicular to 4x-2y=14

....we also want the line to pass through a certain point....that is important because we can use the "point-slope" version of a line to find the equation of the 2nd line....like so.....

y−y1=m(x−x1).......y-4=-1/2 (x - 2)......or y - 4= -1/2 (x-2)......or y -4 = -1/2 x + 1

....add 4 to both sides......we have.....Y = -1/2 x + 1 + 4....y = -1/2 x + 5

..check the point (2,4)...4= -1/2 (2) + 5 = 4 = 4..it checks perfectly....

so the line 4x-2y=14 (or y = 2x - 7) ....

....IS PERPENDICULAR TO THE LINE...

.....y = -1/2 x + 5.....Correct?

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You can also GRAPH both of these lines to literally SEE the perpendicular lines cross each other......