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

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### 4 Answers

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).

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**

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.**

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)