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