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

If you insert both points into y=mx+b you receive
I:19=4m+b
II:24=9m+b
subtraction of I from II to eliminate b:
5=5m
m=1
insert this in I again:
19=4m+b
19=4+b
15=b

-> y=x+15

Answer 2

Answer:

$f(x)=x+15$

Step-by-step explanation:

To find the linear function, we use the slope-intercept form:

$y=mx+b$

So, first we have to find the slope, using the given points:

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{24-19}{9-4}=\frac{5}{5}=1$

Now, we use the point-slope formula to find the equation. We need to use the slope and one point:

$y-y_{1}=m(x-x_{1})\\ y-19=1(x-4)\\y=x-4+19\\y=x+15$

Therefore, the linear function is $f(x)=x+15$, which has a positive slope equal to 1, indicating increase, and the y-axis interception is at y=15.