Witch one has a proportional relationship
Y=1/3 x
Y=x +3
Y=3x + 1
Y= x/3 - 3
The equation y = 1/3x has a proportional relationship because as x increases, y increases at a constant rate of 1/3.
Derive the equation 1,-1 0,-4
To derive the equation, we can find the slope between the two points given: (1, -1) and (0, -4).
The formula for finding the slope between two points (x1, y1) and (x2, y2) is given by:
slope = (y2 - y1) / (x2 - x1)
Plugging in the values from the two points you provided, we get:
slope = (-4 - (-1)) / (0 - 1) = (-4 + 1) / -1 = -3 / -1 = 3
Now that we have the slope, let's write the equation in point-slope form using one of the given points, say (1, -1):
y - y1 = m(x - x1)
Plugging in the values, we get:
y - (-1) = 3(x - 1)
y + 1 = 3(x - 1)
y + 1 = 3x - 3
y = 3x - 4
Therefore, the equation derived from the points (1, -1) and (0, -4) is y = 3x - 4.
Write the equation in slope form 0,1 1,-4
To write the equation in slope-intercept form y = mx + b, where m is the slope and b is the y-intercept, we first need to calculate the slope (m) using the two points provided: (0, 1) and (1, -4).
The formula for slope is:
m = (y₂ - y₁) / (x₂ - x₁)
Plugging in the values:
m = (-4 - 1) / (1 - 0)
m = -5/1
m = -5
Now that we have the slope, we can use one of the points to find the y-intercept (b). Let's use the point (0, 1):
1 = -5(0) + b
1 = b
Now that we have the slope and the y-intercept, the equation of the line is:
y = -5x + 1
Therefore, the equation in slope-intercept form for the points (0, 1) and (1, -4) is y = -5x + 1.