Question

question 4

graph the equation \\(y = \frac{2}{3}x + 1\\) on the coordinate plane.

questions 5

solve the equation for x. show your work.

\\(3(x - 4) = 2x + 5\\)

Explanation:

Identify the y-intercept and slope

The first equation is:

$$y = \frac{2}{3}x + 1$$

The y-intercept is \(b = 1\), giving the point \((0, 1)\).
The slope is \(m = \frac{2}{3}\), meaning "rise 2, run 3".

Find additional points for graphing

Starting from \((0, 1)\):

• Move right 3 units and up 2 units to get \((3, 3)\).
• Move left 3 units and down 2 units to get \((-3, -1)\).

These points define the line on the coordinate plane.

Distribute the terms in the second equation

The second equation is:

$$3(x - 4) = 2x + 5$$

Distribute the 3 on the left side:

$$3x - 12 = 2x + 5$$

Isolate the variable x

Subtract \(2x\) from both sides:

$$x - 12 = 5$$

Add 12 to both sides:

$$x = 17$$

Answer:

Question 4

To graph the equation \(y = \frac{2}{3}x + 1\), plot the y-intercept at \((0, 1)\). From there, use the slope \(\frac{2}{3}\) to plot another point at \((3, 3)\) and draw a straight line through these points.

Question 5

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