2 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

2 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.

https://www.teacherspayteachers.com/Product/Drawing-Algebraic-Straight-line-Graphs-171852 (Links to an external site.)Links to an external site.

https://www.mathwarehouse.com/algebra/linear_equation/slope-of-a-line.php (Links to an external site.)Links to an external site.