24. Write an equation to represent the table below. Please help!!!

y = 2x + 8

Step-by-step explanation:

Using two ordered pairs from the table: (4, 16) and (8, 24):

Let (x1, y1) = (4, 16)

(x2, y2) = (8, 24)

We can start by solving for the slope of the line by using the formula:

Therefore, the slope of the line is 2.

Next, we must determine the y-intercept of the line. By definition, the y-intercept is the y-coordinate of the point where the graph of the linear equation crosses the y-axis. The y-intercept is also the value of y when x = 0.

Using the slope (m) = 2, and one of the points on the given table, (4, 16), we can plug in these values into the slope-intercept form: y = mx + b

y = mx + b

16 = 2(4) + b

16 = 8 + b

Subtract 8 on both sides of the equation to solve for the y-intecept, b:

16 - 8 = 8 + b - 8

8 = b

Now that we have our slope, m = 2, and y-intercept, b = 8, we can establish our linear equation in slope-intercept form:

y = 2x + 8

c. y = 1/4 x + 5

step-by-step explanation:

first, put the equation of the line on the graph into slope-intercept form

(y = mx + b):   y = -4x + 8

second, a perpendicular line has to have "an opposite/reciprocal slope" to the original slope. so, find the "m" value in your original equation (it's -4, right? )

original slope: m = -4   perpendicular slope: change the sign to its opposite and find the reciprocal ("flip" the number)

new slope is now positive (b/c the original slope was negative 4), and it's 1/4 (not the original slope of 4 or 4/1)

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step-by-step explanation: