Question

What value for b would make this equation proportional???

y=3x+b

Answer 1

[AI-generated answer — Bot GPT 3.5]

In order for the equation to be proportional, the value of b must be zero.

If b is not zero, then the equation y=3x+b is not proportional because the y-intercept (b) contributes a constant value to the output y, regardless of the input x.

Answer 2

on a chart, there is a line with points being: (1, 8), (0, 4)

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

Answer 3

[AI-generated answer — Bot GPT 3.5]

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

The slope (m) can be calculated using the formula:
m = (y2 - y1) / (x2 - x1)

Given the points (1, 8) and (0, 4), we can substitute these values into the formula:

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

Now that we have the slope, we can use one of the points to find the y-intercept (b). Let's choose point (0, 4) and substitute the slope (m) and the coordinates of the point into the slope-intercept form equation:

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

Therefore, the equation of the line in slope-intercept form is:
y = 4x + 4