Questions: Graph this line: y-3=-5(x-6) Click to select points on the graph.

Transcript text: Graph this line: \[ y-3=-5(x-6) \] Click to select points on the graph.

Solution

Solution Steps

Step 1: Convert the equation to slope-intercept form

The given equation is in point-slope form: y - 3 = -5(x - 6). To convert to slope-intercept form (y = mx + b), first distribute the -5 on the right side: y - 3 = -5x + 30. Then, add 3 to both sides to isolate y: y = -5x + 33.

Step 2: Identify the y-intercept

In the equation y = -5x + 33, the y-intercept is 33 (the value of 'b' in the slope-intercept form). This means the line crosses the y-axis at the point (0, 33). This point is not on the visible graph.

Step 3: Identify another point on the line

We can choose any x-value and substitute it into the equation to find the corresponding y-value. Let's choose x = 6 (since it was part of the original point-slope equation).
y = -5(6) + 33
y = -30 + 33
y = 3. So, the point (6, 3) is on the line.

Step 4: Plot the points and draw the line

Since the y-intercept (0,33) is off the given graph, we can use the point (6,3) we calculated, and also find another point. If we take x=7, y= -5(7) + 33 = -35+33=-2, so point (7,-2) is also on the line. The plotted points (6,3) and (7,-2) help to locate the line on the provided graph.

Final Answer:

The graph of the line y - 3 = -5(x - 6) can be found by plotting the points (6,3), (7,-2) (or other easily calculated points) since these lie within the given range of the graph. The line will have a slope of -5 and will pass through these calculated points.

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