Question

Write 4 symbolic rules in different forms for a line that goes through the point (-6, -4) and the point (3,8).

a) y = (2/3)x + 4

b) y = -2x + 8

c) y = (4/9)x + 8

d) y = -2x - 4

Answer 1

None of the given symbolic rules (a, b, c, d) match the line through the points (-6, -4) and (3, 8). The correct equation of this line is y = (4/3)x + 4, as calculated from the slope and y-intercept.

Step-by-step explanation:

To determine if the given symbolic rules represent the same line that passes through the points (-6, -4) and (3,8), we must write the equation of the line using these two points and then compare the resultant equation with the given options. The general form of a linear equation is y = mx + b, where 'm' is the slope and 'b' is the y-intercept.

First, we find the slope (m) of the line using the formula: m = (y2 - y1) / (x2 - x1). Plugging in the points (-6, -4) and (3,8), we get: m = (8 - (-4)) / (3 - (-6)) = 12 / 9 = 4/3.

Now, using one of the points and the slope, we can find 'b' by plugging them into the equation y = mx + b and solving for b:

-4 = (4/3)(-6) + b
-4 = -8 + b
b = 4

So, the equation of the line is y = (4/3)x + 4. This equation is not the same as any of the given options (a, b, c, d) which means none of the options given are correct.