(2,5) , (1,3) , (0,1) , (-1,-1) , (-2,-3)
This is a _____ relationship. The y-intercept is _______ and the slope ______ is. The equation of the line is slope-intercept form is ______.
This is a linear relationship.
The y-intercept is 1.
The slope is -2.
The equation of the line in slope-intercept form is y = -2x + 1.
This is a linear relationship. The y-intercept is 1 and the slope is -2/1. The equation of the line in slope-intercept form is y = -2x + 1.
To determine the relationship of the given points, we need to evaluate the pattern or trend among them. In this case, we can calculate the slope (m) between each pair of points to find any consistent change in the y-values as the x-values vary.
To calculate the slope between two points (x1, y1) and (x2, y2), we use the formula:
m = (y2 - y1) / (x2 - x1)
Let's calculate the slopes for the given points:
m1 = (5 - 3) / (2 - 1)
= 2 / 1
= 2
m2 = (3 - 1) / (1 - 0)
= 2 / 1
= 2
m3 = (1 - (-1)) / (0 - (-1))
= 2 / 1
= 2
m4 = (-1 - (-3)) / (-1 - (-2))
= 2 / 1
= 2
As you can see, the slope between each pair of points is 2. This means that there is a consistent change of 2 units in the y-values for every 1 unit change in the x-values.
Next, let's find the y-intercept (b). The y-intercept is the point where the line crosses the y-axis. To find the y-intercept, we can choose any of the given points and substitute its coordinates into the slope-intercept form of a linear equation: y = mx + b. We can use point (2,5) for this calculation:
5 = (2)(2) + b
Solving for b:
5 = 4 + b
b = 5 - 4
b = 1
Therefore, the y-intercept is 1.
We now have the slope (m = 2) and the y-intercept (b = 1). Substituting these values into the slope-intercept form of a linear equation (y = mx + b), we can write the equation of the line:
y = 2x + 1
So, the equation of the line in slope-intercept form is y = 2x + 1.