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Identify the slope and y-intercept of each of the following lines. Then graph each line.

6x + 2y = 12
attached graph
I am confused...

Identify the slope and y-intercept of each of the following lines. Then graph each-example-1

2 Answers

6 votes

Answer:

y=6−3x

y=mx+b

y=−3x+6

Find the values of m and b using the form y=mx+b.

m=−3

b=6

Graph the line using the slope and the y-intercept, or the points.

Slope: −3

y-intercept: (0,6)

x, y

0,6

2,0

Explanation:

hope this helps

Identify the slope and y-intercept of each of the following lines. Then graph each-example-1
User Theadam
by
3.5k points
12 votes

Answer:

Below!

Explanation:

The provided equation is in standard form. To convert it to slope intercept form, we need to have the y-variable isolated (as much as possible) on the L.H.S. Let's start the process by subtracting 6x both sides. This will isolate the y-variable and the cooeficient of the y-variable.

  • ⇒ 6x + 2y = 12
  • ⇒ 6x - 6x + 2y = 12 - 6x
  • ⇒ 2y = 12 - 6x

To further isolate the "y" variable, let's divide 2 both sides. This will isolate the cooeficient of the y-variable. Once the cooeficient of the y-variable is fully isolated, we simply need to simplify the R.H.S (If needed). Then, the equation obtained is in slope intercept form.

  • ⇒ 2y/2 = 12/2 - 6x/2
  • ⇒ y = 12/2 - 6x/2

LIkewise, since the R.H.S can be simplified, let's simplify the R.H.S. The equation we obtained for now is in slope intercept form, but the simplified equation would help us to graph the line.

  • ⇒ y = 12/2 - 6x/2
  • ⇒ y = 6 - 3x

When we look at the slope intercept form formula (y = mx + b), we can see that "6" and "3x" needs to be switched.

  • ⇒ y = -3x + 6 (Slope intercept form)

Finally, lets plot the line on the graph. To plot the line on the graph, we need to determine the x-intercept and the y-intercept.

  • y-intercept: (0, 6)

The x-intercept is the R.H.S of the equation we obtained. Keep in mind that the "y" variable will be 0.

  • ⇒ -3x + 6 = 0

Once we found the solution, we will determine two points of the line and lastly, we will plot the line on the graph.

  • ⇒ -3x + 6 - 6 = 0 - 6
  • ⇒ -3x = -6
  • ⇒ -3x/-3 = -6/-3
  • ⇒ x = 2

Thus, we obtained the following points:

  • x-intercept = 2 ⇒ Point obtained: (2, 0)
  • y-intercept = 6 ⇒ Point obtained: (0, 6)

→ Then, plot these points on the graph. Remember, x coordinate first.

→ Finally, we can draw a line through these points.

And we are done!

Graph:

Identify the slope and y-intercept of each of the following lines. Then graph each-example-1
User Eckymad
by
3.3k points