Line t passes through (4, 5) and is perpendicular to the line shown on the coordinate grid.

a coordinate plane with a line passing through two points at 0 comma 3 and 5 comma 2

what is the equation of line t in standard form?

5x − y = 15
−5x − y = 15
x − 5y = −75
x + 5y = 75

Step-by-step explanation:

step 1

Find the slope of the given line

The formula to calculate the slope between two points is equal to

we have

(0,3) and (5,2)

substitute

step 2

Find the slope of the line t

we know that

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)

so

we have

---> slope of the given line

----> slope of line t

step 3

Find the equation of the line t in point slope form

we have

substitute

step 4

Convert to slope intercept form

isolate the variable y

step 5

Convert to standard form

The equation in standard form is equal to

where

A is a positive integer

B and C are integers

so

subtract y both sides

Adds 15 both sides

Rewrite

let's solve your equation step-by-step.

4x+2=2x+12

step 1: subtract 2x from both sides.

4x+2−2x=2x+12−2x

2x+2=12

step 2: subtract 2 from both sides.

2x+2−2=12−2

2x=10

step 3: divide both sides by 2.

2x

2

=

10

2

x=5

step-by-step explanation:

option (b) is correct

step-by-step explanation:

to find the solution of this system, we need to convert it into reduced row-echelon form. we have,

after applying row operations r2 -> r2/2 and r3 -> r3/3, we get,