Question

A line that passes through (3,5) and (4,13)

Answer 1

y = 8x - 19

Explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m =
`(y_(2)-y_(1) )/(x_(2)-x_(1) )`

with (x₁, y₁ ) = (3, 5 ) and (x₂, y₂ ) = (4, 13 )

m =
`(13-5)/(4-3)` =
`(8)/(1)` = 8 , then

y = 8x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (3, 5 )

5 = 8(3) + c = 24 + c ( subtract 24 from both sides )

- 19 = c

y = 8x - 19 ← equation of line

Answer 2

y = 8x-19

Explanation:

The first step is to find the slope.

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

= ( 13-5)/(4-3)

= 8/1

= 8

Then we can use the slope intercept formula.

y = mx+b

y = 8x+b

Substitute a point to find the intercept.

5 = 8*3+b

5 = 24+b

-19 = b

The formula is

y = 8x-19