Graphing Equations Quick Check
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Question
Use the image to answer the question.
An illustration of a coordinate plane with four quadrants shows the x-axis ranging from negative 9 to 9 and the y-axis ranging from negative 11 to 11 in increments of 1. A solid upward line with arrows at both ends is plotted on the graph. The line passes through the plotted points left parenthesis 0 comma negative 4 right parenthesis and left parenthesis 1 comma negative 1 right parenthesis.
Using the graph, derive the equation of the line in slope-intercept form.
To determine the equation of the line in slope-intercept form, we can use the given points (0, -4) and (1, -1).
First, let's find the slope of the line. The slope (m) is given by the formula:
m = (y2 - y1) / (x2 - x1)
Using the points (0, -4) and (1, -1), we have:
m = (-1 - (-4)) / (1 - 0)
m = 3 / 1
m = 3
So, the slope of the line is 3.
Next, let's use the point-slope form of a line to find the equation of the line. The point-slope form is:
y - y1 = m(x - x1)
Using the point (1, -1) and the slope m = 3, we have:
y - (-1) = 3(x - 1)
y + 1 = 3x - 3
Finally, let's rearrange the equation into slope-intercept form (y = mx + b), where b is the y-intercept:
y + 1 = 3x - 3
y = 3x - 3 - 1
y = 3x - 4
Therefore, the equation of the line in slope-intercept form is y = 3x - 4.
Graphing Equations Quick Check
2 of 52 of 5 Items
Question
Use the image to answer the question.
An illustration of a coordinate plane with four quadrants shows the x-axis ranging from negative 9 to 9 and the y-axis ranging from negative 11 to 11 in increments of 1. A solid downward line with arrows at both ends is plotted on the graph. The line passes through the plotted points left parenthesis 0 comma 1 right parenthesis and left parenthesis 1 comma negative 4 right parenthesis.
Write the equation of the line in slope-intercept form.
To determine the equation of the line in slope-intercept form, we can use the given points (0, 1) and (1, -4).
First, let's find the slope of the line. The slope (m) is given by the formula:
m = (y2 - y1) / (x2 - x1)
Using the points (0, 1) and (1, -4), we have:
m = (-4 - 1) / (1 - 0)
m = -5 / 1
m = -5
So, the slope of the line is -5.
Next, let's use the point-slope form of a line to find the equation of the line. The point-slope form is:
y - y1 = m(x - x1)
Using the point (0, 1) and the slope m = -5, we have:
y - 1 = -5(x - 0)
y - 1 = -5x
Finally, let's rearrange the equation into slope-intercept form (y = mx + b), where b is the y-intercept:
y - 1 = -5x
y = -5x + 1
Therefore, the equation of the line in slope-intercept form is y = -5x + 1.
Graph the linear equation y=−3x+2.(1 point)
To graph the linear equation y = -3x + 2, we can start by plotting a few points and then connecting them to form a line.
We can choose any values for x and substitute them into the equation to find the corresponding y-values.
Let's choose three values for x: x = -1, x = 0, and x = 1.
When x = -1:
y = -3(-1) + 2
y = 3 + 2
y = 5
So, one point on the graph is (-1, 5).
When x = 0:
y = -3(0) + 2
y = 0 + 2
y = 2
So, another point on the graph is (0, 2).
When x = 1:
y = -3(1) + 2
y = -3 + 2
y = -1
So, the third point on the graph is (1, -1).
Now, let's plot these three points on the coordinate plane and connect them with a line:
- y-axis
|
|
1 | x (1, -1)
|
0 | x (0, 2)
|
-1| x (-1, 5)
|
|
|x-axis
After plotting the points and connecting them, we will have a line that goes through (-1, 5), (0, 2), and (1, -1).
Use the image to answer the question.
A coordinate plane shows the x-axis ranging from negative 9 to 9 in increments of 1 and the y-axis ranging from 11 to negative 11 in increments of 1. A line with arrows at both ends joins two plotted points.
The coordinates of the plotted points are as follows: left parenthesis 0 comma 3 right parenthesis, and left parenthesis 3 comma 2 right parenthesis.
Is this the correct graph of y=−13x+4?(1 point)
To verify if the graph represents the equation y = -13x + 4, we can compare the slope of the line in the graph with the slope in the given equation.
The equation y = -13x + 4 is in slope-intercept form (y = mx + b), where m represents the slope of the line.
Comparing the given equation with the standard form, we can see that the slope (m) of the line is -13.
Now, let's calculate the slope of the line on the graph using the two given points: (0, 3) and (3, 2).
The slope (m) is given by the formula:
m = (y2 - y1) / (x2 - x1)
Using the points (0, 3) and (3, 2), we have:
m = (2 - 3) / (3 - 0)
m = -1 / 3
Comparing this slope (-1/3) with the slope in the given equation (-13), we can see that they are not equal.
Therefore, the graph shown does not represent the equation y = -13x + 4.
what is the answer
The graph shown does not represent the equation y = -13x + 4.
now use the options
A. Yes, it is the correct graph because this graph has a y-intercept of (0,3).
B. No, it is not the correct graph because this graph used (0,3) as the y-intercept.
C. No, it is not the correct graph because this graph has a positive slope.
D. Yes, it is the correct graph because this graph has a y-intercept of (0,4).