Given the equation y = - 2x + 2, what is the slope? Write your answer as an integer.
The slope is__
The slope is -2.
Given the equation y = 3/4x - 2 what is the y-intercept? Write your answer as an ordered pair.
The y-intercept is (__).
The y-intercept is (0, -2).
(1, -1)
(0, -4)
Derive the equation of the line in slope-intercept form.
To derive the equation of the line in slope-intercept form, we first need to find the slope.
The slope (m) can be found using the formula:
m = (y2 - y1) / (x2 - x1)
Using the given points:
m = (-1 - (-4)) / (1 - 0)
m = (-1 + 4) / 1
m = 3/1
m = 3
So, the slope of the line is 3.
Now, we can use the slope-intercept form of a linear equation:
y = mx + b
Where m is the slope and b is the y-intercept.
Using one of the given points (0, -4), we can substitute the values into the equation to solve for b:
-4 = 3(0) + b
-4 = 0 + b
b = -4
Therefore, the equation of the line in slope-intercept form is:
y = 3x - 4
(0, 1)
(1, -4)
Write the equation of the line in slope-intercept form.
To find the equation of the line in slope-intercept form, we need to find the slope and the y-intercept.
The slope (m) can be found using the formula:
m = (y2 - y1) / (x2 - x1)
Using the given points:
m = (-4 - 1) / (1 - 0)
m = (-4 - 1) / 1
m = -5/1
m = -5
So, the slope of the line is -5.
To find the y-intercept (b), we can use one of the given points (0, 1) and substitute the values into the slope-intercept form equation:
y = mx + b
1 = -5(0) + b
1 = 0 + b
b = 1
Therefore, the equation of the line in slope-intercept form is:
y = -5x + 1
Graph the linear equation y = - 3x + 2.
To graph the linear equation y = -3x + 2, we can plot some points and draw a line through them.
We can start by finding the y-intercept, which is 2. This means that the line intersects the y-axis at the point (0, 2).
Next, we can find another point on the line by plugging in a value for x and solving for y. Let's choose x = 1:
y = -3(1) + 2
y = -3 + 2
y = -1
So, we have another point on the line: (1, -1).
We can now plot these two points on a graph:
(0, 2)
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___________ (1, -1)
Using these two points, we can draw a straight line through them to graph the equation y = -3x + 2.
The graph of the linear equation y = -3x + 2 is a downward-sloping line passing through the points (0, 2) and (1, -1).
(0,3)
(3,2)
Is this the correct graph of y = - 1/3x + 4?