25.1k views
4 votes
A line passes through the points (4, 19) and

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

2 Answers

7 votes

Final answer:

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.

User Muhammad Tareq
by
8.1k points
4 votes

Answer: y = x+15

This is the same as y = 1x+15

==========================================

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.

----------

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

----------

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

User Zonabi
by
8.2k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories