Question

What value for b would make this equation proportional? Y= 3x + b

Answer 1

[AI-generated answer — Bot GPT 3.5]

If the equation is proportional, it means that the ratio between y and x remains constant. In this case, the ratio between y and x is given by the coefficient of x, which is 3.

For the equation to be proportional, the slope of the equation needs to be equal to the coefficient of x, which means b should be equal to 0.

Therefore, the value of b that would make the equation proportional is b = 0.

Answer 2

Derive the equation in slope form 0,4 1,9

Answer 3

[AI-generated answer — Bot GPT 3.5]

To find the equation in slope-intercept form (y = mx + b) given the two points (0,4) and (1,9), we first need to find the slope (m) of the line using the formula:

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

Substitute the coordinates of the two points:

m = (9 - 4) / (1 - 0)
m = 5/1
m = 5

Now that we have the slope, we can use one of the points (0,4) to find the y-intercept (b). Substitute the values into the slope-intercept form equation and solve for b:

4 = 5(0) + b
4 = 0 + b
b = 4

Therefore, the equation in slope-intercept form is:

y = 5x + 4

Answer 4

0,4 1,8

Answer 5

[AI-generated answer — Bot GPT 3.5]

To find the equation in slope-intercept form (y = mx + b) given the two points (0,4) and (1,8), we first need to find the slope (m) of the line using the formula:

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

Substitute the coordinates of the two points:

m = (8 - 4) / (1 - 0)
m = 4/1
m = 4

Now that we have the slope, we can use one of the points (0,4) to find the y-intercept (b). Substitute the values into the slope-intercept form equation and solve for b:

4 = 4(0) + b
4 = 0 + b
b = 4

Therefore, the equation in slope-intercept form is:

y = 4x + 4

Answer 6

Slope intercept form 0,-2. 3,0

Answer 7

[AI-generated answer — Bot GPT 3.5]

To find the equation in slope-intercept form (y = mx + b) given the two points (0, -2) and (3, 0), first calculate the slope using the formula:

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

Substitute the coordinates of the two points:

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

Now that we have the slope, we can use one of the points (0, -2) to find the y-intercept (b). Substitute the values into the slope-intercept form equation and solve for b:

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

Therefore, the equation in slope-intercept form is:

y = (2/3)x - 2