ALGEBRA FOLLOW-UP
MO-MO2 discussion posts follow-up.
Here's the 1st one:
As you have shown above Ax + By = C can be converted into y = mx + b format.
Keep "By" on the left hand side of the equation and move "Ax" to the right side, we get,
By = - Ax + C
Divide both side of equation by B,
By/B = -Ax/B + C/B
y = (-A/B)x + (C/B)
Slope (m) = -A/B and y-intercept (b) = C/B
Similarly, we can convert -4x = -2y - 8 to y = mx + b form.
2y = 4x - 8
2y/2 = 4x/2 - 8/2
y = 2x - 4
Slope (m) = 2 and b = -4
We can get two points to plot a graph, when x = 0, y = -4 and when y = 0, x = 2
We can also plot a graph using slope (m = 2) and y-intercept (b = -4)
Lets start with y-intercept point, b = -4 (this will be our first point)
since our slope, m = 2 or 2/1, go up 2 units from y-intercept (on y-axis),
-4+2 = -2, and go right 1 unit (x-axis)
So our coordinates will be (0, -4) and (1,-2)
Verify the points on the equation: y = 2x - 4
(0, -4),
- 4 = 2(0) - 4
-4 = -4 OK.
(1,-2)
-2 = 2(1) - 4
-2 = 2 - 4
-2 = -2 OK.
2nd:
Professor and Class,
The linear equation I am discussing is y=3x-5. To set the x-intercept, y = 0
y=3x-5
0=3x-5
5=3x
5/3=x
(5/3, 0) is the x intercept
to set the y intercept, x=0
y=3x-5
y=3(0)-5
y=-5
(0,-5) is the y intercept
as shown in below graph:
or rise/run
m=−5−0/2−1m=−5−0/2−1
m=-5
the slope is undefined.
References
OpenStax College. (2015). College Algebra. Houston, TX: OpenStax CNX. Retrieved from https://openstax.org/details/books/college-algebrLinks to an external site.
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