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

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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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

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