Determining an Equation of a Line 8-5
Write an equation of a line that has slope 2 and y-intercept 3
Easy! remember y = mx + b
just substitute in what you have… y = 2x + 3
Write an equation of a line that has slope -4 and x-intercept 3.
This is a little different.
The x-intercept is the x-coordinate of the point where a line crosses the x-axis. So here the point must be (3,0) so now you can substitute into y=mx + b and find b.
First substitute in -4 for m y = -4x +b
To find b , substitute 3 for x and 0 for y in y = -4x + b
so
0=-4(3) + b
0=-12 + b
12=b
Therefore the equation must be y = -4x + 12
Write an equation of the line passing through the points ( -2, 5) and ( 4, 8)
Since it doesn't give us the slope, we must find it using
Substitute ½ for m in y = mx + b
y = x/2 + b
Choose one of the points, say (4, 8) and substitute 4 for x and 8 for y.
8 = (1/2)(4) + b
8 = 2 + b
6 = b
Therefore the equation is y = (1/2)x + 6
or y = x/2 + 6
Note: that we could have used the point ( -2, 5) and the resulting equation would have been the same!
Write an equation in STANDARD FORM for the following line described
The line that is parallel to x – 2y + 7 = 0 and contains ( -4, 0)
The first thing we need to do is change the given line into slope-intercept form
y = mx + b
-2y = -x – 7 becomes y = x/2 + 7/2
If the line we are trying to find is parallel to that line its slope must also be ½
Now using y = mx + b and the point on the line
0 = (1/2)(-4) + b
0= -2 + b
b = 2
so the line is y = x/2 + 2
BUT that is not in standard form Ax + By = C
Where A, B, and C are integers and A is a whole number
-x/2 + y = 2
Now multiply everything by -2
x- 2y = -4
Find a line passing through ( -2, 3), (2, 5) and (6, k) Find k
First find the slope using the two given points
y = (1/2)x +b
Using ( -2,3)
3 = (1/2)(-2) + b
3 = -1 + b
4 = b
y = (1/2)x + 4 is the equation of the line so to solve for k
k = (1/2)(6) + 4
k = 3 + 4 = 7
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