which is the graph of the equation y - 1 = 2/3(x - 3)?

Answer:

The graph of the equation (y - 1=\frac{2}{3}(x - 3)) is a straight - line. We can rewrite the equation in slope - intercept form (y=mx + b) (where (m) is the slope and (b) is the y - intercept).

First, distribute the (\frac{2}{3}) on the right - hand side: [ \begin{align*} y-1&=\frac{2}{3}(x - 3)\ y-1&=\frac{2}{3}x-2 \end{align*} ]

Then, add 1 to both sides of the equation: [y=\frac{2}{3}x-1]

The slope (m = \frac{2}{3}) and the y - intercept (b=-1).

We can also use the point - slope form to check points on the line. The point - slope form (y - y_1=m(x - x_1)) tells us that the line passes through the point ((x_1,y_1)=(3,1)) (by comparing (y - 1=\frac{2}{3}(x - 3)) with (y - y_1=m(x - x_1))).

Let's check the points given in the graph:

• For the point ((3,1)): Substitute (x = 3) into (y-1=\frac{2}{3}(x - 3)), we get (y-1=\frac{2}{3}(3 - 3)=0), so (y = 1).
• For the point ((-3,-3)): Substitute (x=-3) into (y-1=\frac{2}{3}(x - 3)), we have (y-1=\frac{2}{3}(-3 - 3)=\frac{2}{3}\times(-6)=-4), then (y=-3).

We can plot the y - intercept ((0,-1)) and use the slope (\frac{2}{3}) (rise 2, run 3) to draw the line.

Explanation:

Step1: Rewrite in slope - intercept form

[y-1=\frac{2}{3}(x - 3)\Rightarrow y=\frac{2}{3}x-1]

Step2: Identify slope and y - intercept

Slope (m=\frac{2}{3}), y - intercept (b = - 1)

Step3: Check given points

Use point - slope form to check if points lie on line.