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 2 right parenthesis and left parenthesis 1 comma 3 right parenthesis.
Use the graph to derive the equation of the line in slope-intercept form.
(1 point)
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To find the equation of the line in slope-intercept form, we need to determine the slope and the y-intercept.
First, let's find the slope. The slope (m) is given by the formula:
m = (y2 - y1) / (x2 - x1)
Using the two given points on the line, (-2,0) and (3,1), we can plug in the values:
m = (1 - 0) / (3 - (-2))
m = 1 / 5
So, the slope of the line is 1/5.
Next, let's find the y-intercept. The y-intercept (b) is the value of y when x = 0. From the graph, we can see that the line passes through the point (0,-2). Therefore, the y-intercept is -2.
Now we can write the equation of the line in slope-intercept form, which is y = mx + b:
y = (1/5)x - 2
Therefore, the equation of the line in slope-intercept form is y = (1/5)x - 2.
Graph the linear equation y=2x−3.(1 point)
Responses
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 negative 1 right parenthesis and left parenthesis 1 comma negative 3 right parenthesis.
Image with alt text: 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 negative 1 right parenthesis and left parenthesis 1 comma negative 3 right parenthesis.
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 1 right parenthesis, and left parenthesis 1 comma 4 right parenthesis.
Image with alt text: 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 1 right parenthesis, and left parenthesis 1 comma 4 right parenthesis.
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 1 comma negative 1 right parenthesis, and left parenthesis 0 comma negative 3 right parenthesis.
Image with alt text: 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 1 comma negative 1 right parenthesis, and left parenthesis 0 comma negative 3 right parenthesis.
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 3 right parenthesis and left parenthesis 1 comma 5 right parenthesis.
Image with alt text: 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 3 right parenthesis and left parenthesis 1 comma 5 right parenthesis.
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To graph the linear equation y = 2x - 3, we can use the information given in the image.
The line passes through the points (0, 1) and (1, 4), so we can plot these points on the graph.
On the x-axis, locate the points (0, 1) and (1, 4).
Next, draw a straight line passing through these points. The line should be upward-sloping.
Label the line as y = 2x - 3.
The graph should show a solid upward line passing through the points (0, 1) and (1, 4).
Write y−6x=5 in slope-intercept form(1 point)
y=
To write the equation y - 6x = 5 in slope-intercept form, we need to isolate y on one side of the equation.
First, let's move the -6x term to the other side by adding 6x to both sides:
y - 6x + 6x = 5 + 6x
Simplifying, we have:
y = 6x + 5
Therefore, the equation y - 6x = 5 in slope-intercept form is y = 6x + 5.
Describe what makes a proportion. Give an example of a proportion.(2 points)
A proportion is a statement that two ratios or fractions are equal. In a proportion, the ratio of the first two terms (called the antecedents) is equal to the ratio of the last two terms (called the consequents).
Mathematically, a proportion can be represented as:
a/b = c/d
where a, b, c, and d are numbers.
For example, let's consider the following proportion:
2/5 = 6/15
In this proportion, the ratio of 2 to 5 is equal to the ratio of 6 to 15. We can cross-multiply to check:
2 * 15 = 5 * 6
30 = 30
Since both sides are equal, we can say that the proportion is true.