Write the linear equation that gives the rule for this table.
x y
1 -33
2 -28
3 -23
4 -18
Write your answer as an equation with y first, followed by an equals sign.
What is the linear equation that gives the rule for this table?y = -5x – 38
Share
To find the linear equation from the given table, we can use the formula for a linear equation in the form of (y = mx + b), where (m) is the slope and (b) is the y-intercept.
1. Finding the slope (m):
Choose two points from the table. For instance, the points (1, -33) and (2, -28).
– The formula for slope (m) is:
[
m = frac{y_2 – y_1}{x_2 – x_1}
]
– Plugging in the values:
[
m = frac{-28 – (-33)}{2 – 1} = frac{5}{1} = 5
]
2. Finding the y-intercept (b):
We can use one of the points and the slope to find (b). Using the point (1, -33):
– Substitute (x) and (y) into the equation:
[
-33 = 5(1) + b
]
– Solving for (b):
[
-33 = 5 + b implies b = -33 – 5 = -38
]
3. Writing the equation:
Now we have (m = 5) and (b