Question

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

(3,0) (0,-2)

Answer 1

[AI-generated answer — Bot GPT 3.5]

To write 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:

m = (y2 - y1) / (x2 - x1)

Using the points (3,0) and (0,-2), we have:

m = (-2 - 0) / (0 - 3)
m = -2 / -3
m = 2/3

Next, we know that the slope-intercept form of a line is given by:

y = mx + b

where m is the slope and b is the y-intercept.

We can substitute the known values of the slope and one of the points (such as (3,0)) into the equation to find the y-intercept.

0 = (2/3)(3) + b
0 = 2 + b
b = -2

So the equation of the line in slope-intercept form is:

y = (2/3)x - 2

Answer 2

[AI-generated answer — Step-by-Step Bot]

To write the equation of a line in slope-intercept form (y = mx + b), we need to find the slope (m) and the y-intercept (b).

Step 1: Find the slope (m)
The slope (m) can be found using the formula:
m = (y2 - y1) / (x2 - x1)

Using the points (3,0) and (0,-2), we can substitute the values into the formula:

m = (0 - (-2)) / (3 - 0)
m = 2 / 3

So the slope (m) is 2/3.

Step 2: Find the y-intercept (b)
The y-intercept (b) is the value of y when x = 0.
We know that one of the points on the line is (0, -2), so the y-intercept is -2.

Step 3: Write the equation in slope-intercept form
Now that we have the slope (m = 2/3) and the y-intercept (b = -2), we can write the equation of the line in slope-intercept form (y = mx + b):

y = (2/3)x - 2

Therefore, the equation of the line in slope-intercept form is y = (2/3)x - 2.

Answer 3

[AI-generated answer — Explain Bot]

To find the equation of the line in slope-intercept form (y = mx + b), we need to determine the values of slope (m) and y-intercept (b).

The formula to calculate the slope (m) between two points (x1, y1) and (x2, y2) is:

m = (y2 - y1) / (x2 - x1)

In this case, the given points are (3, 0) and (0, -2). Substituting the coordinates into the formula:

m = (-2 - 0) / (0 - 3)
m = -2 / -3
m = 2/3

Therefore, the slope (m) is 2/3.

To find the y-intercept (b), we can choose either of the given points (3, 0) or (0, -2) and substitute the values of x, y, and m into the slope-intercept form equation:

0 = (2/3)(3) + b
0 = 2 + b
b = -2

So, the y-intercept (b) is -2.

Now we have the values of m = 2/3 and b = -2. We can substitute these values into the slope-intercept form equation (y = mx + b):

y = (2/3)x - 2

Hence, the equation of the line in slope-intercept form is y = (2/3)x - 2.