(1, 8)
(0, 4)
Derive 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.
First, let's find the slope using the formula:
slope = (change in y) / (change in x)
The change in y is 8 - 4 = 4
The change in x is 1 - 0 = 1
slope = 4 / 1 = 4
Now that we have the slope, we can use the point-slope form of a line to find the equation:
y - y1 = m(x - x1)
where (x1, y1) is a point on the line and m is the slope.
Let's choose the point (0, 4) as the point on the line. Plugging this into the equation, we get:
y - 4 = 4(x - 0)
Simplifying, we get:
y - 4 = 4x
To rewrite this equation in slope-intercept form (y = mx + b), we need to isolate y:
y = 4x + 4
So, the equation of the line in slope-intercept form is y = 4x + 4.
(0, 2)
(1, -1)
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.
First, let's find the slope using the formula:
slope = (change in y) / (change in x)
The change in y is -1 - 2 = -3
The change in x is 1 - 0 = 1
slope = -3 / 1 = -3
Now that we have the slope, we can use the point-slope form of a line to find the equation:
y - y1 = m(x - x1)
where (x1, y1) is a point on the line and m is the slope.
Let's choose the point (0, 2) as the point on the line. Plugging this into the equation, we get:
y - 2 = -3(x - 0)
Simplifying, we get:
y - 2 = -3x
To rewrite this equation in slope-intercept form (y = mx + b), we need to isolate y:
y = -3x + 2
So, the equation of the line in slope-intercept form is y = -3x + 2.
(3, 0)
(0, -2)
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.
First, let's find the slope using the formula:
slope = (change in y) / (change in x)
The change in y is -2 - 0 = -2
The change in x is 0 - 3 = -3
slope = -2 / -3 = 2/3
Now that we have the slope, we can use the point-slope form of a line to find the equation:
y - y1 = m(x - x1)
where (x1, y1) is a point on the line and m is the slope.
Let's choose the point (0, -2) as the point on the line. Plugging this into the equation, we get:
y - (-2) = (2/3)(x - 0)
Simplifying, we get:
y + 2 = (2/3)x
To rewrite this equation in slope-intercept form (y = mx + b), we need to isolate y:
y = (2/3)x - 2
So, the equation of the line in slope-intercept form is y = (2/3)x - 2.
Given the equation y = - 2x + 2, what is the slope? Write your answer as an integer.
The slope is__