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 need to find the slope and the y-intercept.
First, let's find the slope using the given coordinates (0, 1) and (1, -4).
Slope (m) = change in y / change in x
= (-4 - 1) / (1 - 0)
= -5 / 1
= -5
Now, we can use the slope-intercept form of a line, which is y = mx + b, where m represents the slope and b represents the y-intercept.
We already have the slope as -5. Now let's calculate the y-intercept (b) using one of the given points.
Using the point (0, 1), we can substitute the x and y values into the equation and solve for b.
1 = -5(0) + b
1 = b
Since b = 1, the y-intercept is 1.
Now, we can write the equation of the line in slope-intercept form:
y = -5x + 1
Looking at the graph:
(3 points)
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a. Triangles ABC and CDE are called Response area
b. The slope of line AE can be written as Response area
c. This is a Response area relationship
a. Triangles ABC and CDE are called congruent triangles.
b. The slope of line AE can be written as undefined.
c. This is a perpendicular relationship.
Look at the graph.
(2 points)
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a. What is the slope of the line? Response area
b. The equation y=−4/3x
was shifted Response area to get the graph of y=−4/3x −5
a. What is the slope of the line? The slope of the line is -4/3.
b. The equation y=−4/3x was shifted 5 units downwards to get the graph of y=−4/3x - 5.
To find the equation of the line in slope-intercept form, we need to determine the slope (m) and the y-intercept (b).
The slope of the line can be calculated using the formula:
m = (change in y) / (change in x)
Given the two plotted points (0, 1) and (1, -4), we can calculate the slope as follows:
m = (-4 - 1) / (1 - 0)
m = -5 / 1
m = -5
Now we have the slope (-5), we can write the equation of the line in slope-intercept form as:
y = mx + b
Using one of the given points (0, 1) and substituting the slope (-5), we can solve for the y-intercept (b):
1 = -5(0) + b
b = 1
Therefore, the equation of the line in slope-intercept form is:
y = -5x + 1
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 of the line. The slope of a line can be calculated using the formula:
slope = (change in y-coordinate) / (change in x-coordinate)
In this case, we have the coordinates of two points on the line: (0, 1) and (1, -4).
Using the coordinates, we can calculate the slope:
slope = (-4 - 1) / (1 - 0) = -5 / 1 = -5
Now that we have the slope, we can proceed to find the y-intercept. The y-intercept is the point where the line intersects the y-axis. From the illustration, we can see that the line passes through the point (0, 1). Therefore, the y-intercept is 1.
Finally, we can write the equation of the line in slope-intercept form: y = mx + b, where m is the slope and b is the y-intercept.
Plugging in the values, we get:
y = -5x + 1
Thus, the equation of the line in slope-intercept form is y = -5x + 1.