there is a table with the contents being:

Question

x: 0 , 9 , 18
y: 3 , 6 , 9

Identify the slope and y -intercept of the line. Provide the most simplified form of the slope.

Answer 1

To calculate the slope, we need to first determine the change in y and the change in x between any two points on the table.

Let's take the first two points (0,3) and (9,6):

Change in y: 6 - 3 = 3
Change in x: 9 - 0 = 9

Now we can calculate the slope:

slope = change in y / change in x
slope = 3/9
slope = 1/3

So, the slope of the line is 1/3.

To find the y-intercept, we can use the point (0,3) which intersects the y-axis. Therefore, the y-intercept is 3.

So, the slope is 1/3 and the y-intercept is 3.

Answer 2

There is a line with points being: (0, -1), (1, 1)

Write the equation of the line in slope-intercept form.

Answer 3

To find the equation of the line in slope-intercept form, we need to first calculate the slope using the given points.

Let's calculate the slope using the points (0, -1) and (1, 1):

slope = (y2 - y1) / (x2 - x1)
slope = (1 - (-1)) / (1 - 0)
slope = 2 / 1
slope = 2

Now that we have the slope, we can write the equation of the line in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.

Using the point (0, -1) to find the y-intercept:

-1 = 2(0) + b
-1 = 0 + b
b = -1

Now we can write the equation of the line:

y = 2x - 1

Therefore, the equation of the line in slope-intercept form is y = 2x - 1.