Question

A line passes through the points (4, 19) and

(9,24). Write a linear function in the form
y= mx + b for this line.

Answer 1

The equation of the line passing through the points (4, 19) and (9, 24) is y = x + 15.

Step-by-step explanation:

The equation of the line passing through the points (4, 19) and (9, 24) can be written in the form y = mx + b, where m represents the slope and b represents the y-intercept.

First, let's calculate the slope (m) using the formula m = (y2 - y1) / (x2 - x1). Substituting the values, we get m = (24 - 19) / (9 - 4) = 5 / 5 = 1.

Now, let's substitute the values of one of the points into the equation to find the y-intercept (b). Using point (4, 19), we get 19 = 1(4) + b. Solving for b, we have b = 19 - 4 = 15.

Therefore, the linear function for the given line is y = x + 15.

Answer 2

Answer: y = x+15

This is the same as y = 1x+15

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Work Shown:

The two given points are

(x1,y1) = (4,19)

(x2,y2) = (9,24)

Use the slope formula

m = (y2-y1)/(x2-x1)

m = (24 - 19)/(9-4)

m = 5/5

m = 1

The slope is 1.

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Pick one of the points and plug those coordinates into y = mx+b along with m = 1. I'll plug (x,y) = (4,19) into the equation

y = mx+b

19 = 1*4+b

19 = 4+b

4+b = 19

b+4 = 19

b+4-4 = 19-4 ... subtract 4 from both sides

b = 15

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m = 1 and b = 15 makes y = mx+b turn into y = 1x+15 or simply y = x+15