Question

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

y + 3 = 2 (x + 4)

Answer 1

• y+3=2(x+4)
• y+3=2x+8
• y=2x+8-3
• y=2x+5

Comapre to slope intercept form y=mx+b

• Slope=m=2
• Y intercept=b=5

Answer 2

Below!

Explanation:

1. Determining the y-intercept of the line:

The provided equation is in point slope form. To determine the slope and the y-intercept, we need to convert the equation to slope intercept form. Once it is converted to slope intercept form, the constant will be the y-intercept of the line. Start out by simplifying the distributive property on the R.H.S.

`\implies y + 3 = 2 (x + 4)`

`\implies y + 3 = (2x + 8)`

Now, open the parenthesis on the R.H.S

`\implies y + 3 = 2x + 8`

If we take a look at the formula of slope intercept form (y = mx + b), we can see that "y" is isolated on the L.H.S. Thus, we need to subtract 3 both sides to isolate the y-variable.

`\implies y + 3 - 3 = 2x + 8 - 3`

`\implies y = 2x + 5`

We can see that the only constant in the equation is 5.

Therefore, 5 is the y-intercept.

2. Determining the slope of the line:

To determine the slope of the line, let's compare the formula with the equation obtained.

`\implies (y = 2x + 5) \ = \ (y = mx + b)`

Thus, we obtain the following:

• y = y
• 2 = m (Slope)
• x = x
• 5 = b (Y-intercept)

Thus, 2 is the slope of the line.

3. Plotting the line on the coordinate plane:

To graph the line on a coordinate plane, plot the y-intercept on the graph. The y-intercept is ALWAYS plotted on the y-axis.

Thus, the y-intercept plotted on graph is (0, 5).

Furthermore, plot a second point on the graph to draw a straight line through those points.

Determining the second point of the line:

If the slope of the line is 2, it means that the run (x) is 1 and the rise (y) is 2. Thus, we can add 1 to the x-coordinate of the y-intercept and 2 to the y-coordinate of the y-intercept.

• ⇒ (0, 5)
• ⇒ x = 0; y = 5
• ⇒ Second point: x = 0 + 1; y = 5 + 2
• ⇒ Second point: x = 1; y = 7
• ⇒ Second point: (1, 7)

Then, plot these points on the coordinate plane. Keep in mind that plot the x coordinate first, then the y-coordinate next. Once the coordinates are plotted, draw a line from the x-coordinate and another line from the y-coordinate. Finally, use your ruler and draw a line that passes through those two points. Your obtained graph is the graph of the line.