Question

9 (\frac{3}{4}x - 3)
which graph correctly represents the equation?
(there are four graphs shown, each with a grid and a line, labeled with options (probably a, b, c, d) but the labels are partially unclear from the ocr. the equation is (\frac{3}{4}x - 3) and the question is about identifying the correct graph.)

Explanation:

Step1: Identify the slope and y-intercept

The equation is in slope - intercept form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. For the equation \(y=\frac{3}{4}x - 3\), the slope \(m=\frac{3}{4}\) (positive, so the line should be increasing from left to right) and the y - intercept \(b=- 3\) (the line crosses the y - axis at \((0,-3)\)).

Step2: Analyze the options based on slope and y - intercept

• For a line with a positive slope (\(\frac{3}{4}>0\)), the line should be rising as we move from left to right. So we can eliminate the options with negative slopes (the lines that are falling from left to right).
• The y - intercept is \(-3\), so the line should cross the y - axis at \(y = - 3\).
• Let's check the y - intercept: The first option has a y - intercept at \(y = 3\) (incorrect), the second option has a y - intercept at \(y=-3\) and a positive slope (since it is rising from left to right), the third and fourth options have negative slopes (incorrect as our slope is positive).

Answer:

The graph with a positive slope (rising from left to right) and y - intercept at \(y = - 3\) (the second graph among the given options, assuming the second graph has these properties).