Question

find the slope and the y-intercept of the line. write fractional answers in lowest terms.

(2y + 6x + 9 = 16 + 6x)

the slope is
the y-intercept is ((0, ))

Explanation:

Simplify the linear equation

We begin with the given equation of the line:

$$2y + 6x + 9 = 16 + 6x$$

Using the Linear Equations concept, we can simplify this equation by subtracting \(6x\) from both sides:

$$2y + 9 = 16$$

Solve for y

Next, we isolate the variable \(y\) to help rewrite the equation in a standard form. Subtract \(9\) from both sides:

$$2y = 16 - 9$$

$$2y = 7$$

Now, divide both sides by \(2\):

$$y = \frac{7}{2}$$

Identify slope and y-intercept

Using the Slope-Intercept Form of a linear equation, which is \(y = mx + b\), we can rewrite our equation as:

$$y = 0x + \frac{7}{2}$$

Comparing this to \(y = mx + b\), we apply the Slope and Y-intercept concept to identify:

• The slope \(m\) is \(0\).
• The y-intercept \(b\) is \(\frac{7}{2}\), which corresponds to the point \((0, \frac{7}{2})\).

Answer:

Find the slope and the y-intercept of the line. Write fractional answers in lowest terms.

\(2y + 6x + 9 = 16 + 6x\)

The slope is <blank>0</blank>.
The y-intercept is (0, <blank>\(\frac{7}{2}\)</blank>).