Answer:
C. y + 4 = -1/2 (x - 1)
Step-by-step explanation:
The x values go up by 6 units each step, 1, 7, 13, 19.
Start with 1 and add 6 to get 7, then add 6 to get 13, then add 6 to get 19.
For each corresponding step in x, y becomes 3 less.
Start with -4, then subtract 3 to get -7, subtract 3 to get -10, subtract 3 to get -13.
For every change of 6 in x, you get a change of -3 in y. This means a linear relationship.
To find the equation, we can use any two of the given points and the point-slope equation of a line.
y - y1 = m(x - x1)
m = slope = (y2 - y1)/(x2 - x1)
where (x1, y1) and (x2, y2) are two points on the line, and m = slope.
Let's use the points (x1, y1) = (1, -4) and (x2, y2) = (7, -7)
y - y1 = (y2 - y1)/(x2 - x1) * (x - x1)
y - (-4) = (-7 - (-4))/(7 - 1) * (x - 1)
y + 4 = (-7 + 4)/(6) * (x - 1)
y + 4 = (-3/6)(x - 1)
y + 4 = -1/2 (x - 1)
