Question

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

Answer 1

Answer:

$5x-y=15$

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

$m=\frac{y2-y1}{x2-x1}$

we have

(0,3) and (5,2)

substitute

$m=\frac{2-3}{5-0}$

$m=\frac{-1}{5}$

$m=-\frac{1}{5}$

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

$m_1*m_2=-1$

we have

$m_1=-\frac{1}{5}$ ---> slope of the given line

$m_2=5$ ----> slope of line t

step 3

Find the equation of the line t in point slope form

$y-y1=m(x-x1)$

we have

$m=5$

$point\ (4,5)$

substitute

$y-5=5(x-4)$

step 4

Convert to slope intercept form

$y=mx+b$

isolate the variable y

$y-5=5x-20$

$y=5x-20+5$

$y=5x-15$

step 5

Convert to standard form

The equation in standard form is equal to

$Ax+By=C$

where

A is a positive integer

B and C are integers

so

$y=5x-15$

subtract y both sides

$0=5x-15-y$

Adds 15 both sides

$15=5x-y$

Rewrite

$5x-y=15$