unit 3 lesson 7 graphing equations
look at the graph
a. what is the slope of the line?
b. the equation y=-4/3x was shifted _ to get the graph of y=-4/3x-5
a. To determine the slope of the line, we can observe the change in y-coordinates over the change in x-coordinates. By counting the rise and run between any two points on the line, we can determine the slope.
b. To shift the graph of y = -4/3x downwards by 5 units, we subtract 5 from the equation: y = -4/3x - 5.
To determine the slope of a line on a graph, you need to calculate the change in the y-coordinates divided by the change in the x-coordinates between two points on the line. Let's find the slope by selecting two points on the line.
Next, we can use these coordinates to calculate the slope using the formula:
slope = (y2 - y1) / (x2 - x1),
where (x1, y1) and (x2, y2) represent the coordinates of the two points on the line.
For the given equation, y = -4/3x, we can see that the coefficient -4/3 is the slope. This means that the slope of the line is -4/3.
To answer part b of your question, we need to identify the transformation that occurred to the original equation y = -4/3x to obtain the equation y = -4/3x - 5.
The original equation, y = -4/3x, represents a line passing through the origin (0,0) with a slope of -4/3.
By subtracting 5 from the equation, we are shifting the entire graph downward by 5 units. This means that each point on the original line is shifted vertically downward by 5 units.
Therefore, the equation y = -4/3x - 5 is obtained by shifting the graph of y = -4/3x downward by 5 units.
To find the slope of the line on the graph, you can look for any two points on the line and use the formula:
slope (m) = (change in y) / (change in x)
Unfortunately, since I cannot see the graph that you are referring to, I am unable to determine the slope.
However, I can help you with part b of your question. To modify the equation y=-4/3x into y=-4/3x-5, the equation was shifted downward by 5 units. This means that the entire line moved down by 5 units, creating a parallel line with a y-intercept of -5.