Write an equation for the line that passes through a point (2,4) with the slope 4?

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samhouston's profile pic

samhouston | Middle School Teacher | (Level 1) Associate Educator

Posted on

The equation for a line in slope-intercept form is:

y = mx + b

where m is the slope and b is the y-intercept.  You are given m and a point.  You can use substitution to find b.

Substitute 4 `->` m, 2 `->` x, and 4 `->` y.

4 = 4 * 2 + b

Now solve for b.

4 = 8 + b

-4 = b

This is your y-intercept.  Therefore the equation for this line is:

y = 4x + -4

This can be checked using a graph:

 

Notice that the line includes the point (2, 4).

 

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The general equation of a line passing through a point (x1, y1) and with a slope m is: (y - y1)/(x - x1) = m

We have to determine the equation of the line that passes through (2, 4) and which has a slope 4.

Here x1 = 2, y1 = 4 and m = 4

(y - 4)/(x - 2) = 4

=> (y - 4) = 4(x - 2)

=> y - 4 = 4x - 8

=> 4x - y - 4 = 0

The equation of the line is 4x - y - 4 = 0

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

First, we'll recall the slope intercept form of the line equation:

y = mx + n, where m represents the slope of the line and n is the y intercept.

Now, we'll fill in the elements provided by enunciation:

4 = 4*2 + n

n = 4 - 8

n = -4

The slope intercept form of the equation of the line is: y = 4x - 4.

Wiggin42's profile pic

Wiggin42 | Student, Undergraduate | (Level 2) Valedictorian

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We want a line that passes through a point (2,4) with the slope 4. 

Given a point and its slope, its best to use the point slope form which in general terms is

y - y1 = m(x - x1) where (x1,y1) is the point and m is the slope. 

Plug in!

y - 4 = 4(x - 2)

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