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

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

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

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

option d. 6x − y = 19

step-by-step explanation:

step 1

find the slope of the given line that passes through the points (0,3) and (6,2)

m=(2-3)/(6-0)

m=-1/6

step 2

find the slope of the line t

we know that

if two lines are perpendicular, then the product of their slopes is equal to -1

m1*m2=-1

we have

m1=-1/6

substitute

(-1/6)*m2=-1

m2=6

step 3

find the equation of the line t

the equation of the line into point slope form is equal to

y-y1=m(x-x1)

we have

m=6

point (4,5)

substitute

y-5=6(x-4)

y=6x-24+5

y=6x-19

6x-y=19

6x-y=19

Step-by-step explanation:

7x − y = 23

Step-by-step explanation:

The equation of line shown using the two points would be:

We know perpendicular line's slope (the number before x) would be "negative reciprocal of this, hence the equation of the perpendicular line would take the form:

Since it goes through (4,5), we can plug in 4 in x and 5 in y to figure out b:

So the equaiton is y = 7x - 23

In standard form it is: 7x - y = 23

6x − y = 19

Step-by-step explanation:

x + 6y = 114

4 + 6(5) = 114

34 = 114 (false)

−6x − y = 19

-6(4) - 5 = 19

-29 = 19 (false)

x − 6y = −11

4 - 6(5) = -11

-26 = -11 (false)

6x − y = 19

6(4) - 5 = 19

19 = 19 (true)

For this case we have that by definition, the equation of a line of the slope-intersection form is given by:

Where:

m: It is the slope of the line

b: It is the cut-off point with the y axis

To find the slope of the plotted line, we need two points, according to the image we have:

The slope is:

Therefore, the equation is of the form:

We substitute one of the points and find "b":

Finally, the equation of the graph is:

By definition, if two lines are perpendicular then the product of their slopes is -1. Thus, the slope of a perpendicular line will be:

Thus, the equation of the line t is of the form:

y = 5x + b

We substitute the point and find "b":

Finally, the equation is of the form:

Option A

[tex]5x-y=15[/tex]

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

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

we have

(0,3) and (5,2)

substitute

[tex]m=\frac{2-3}{5-0}[/tex]

[tex]m=\frac{-1}{5}[/tex]

[tex]m=-\frac{1}{5}[/tex]

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

[tex]m_1*m_2=-1[/tex]

we have

[tex]m_1=-\frac{1}{5}[/tex] ---> slope of the given line

[tex]m_2=5[/tex] ----> slope of line t

step 3

Find the equation of the line t in point slope form

[tex]y-y1=m(x-x1)[/tex]

we have

[tex]m=5[/tex]

[tex]point\ (4,5)[/tex]

substitute

[tex]y-5=5(x-4)[/tex]

step 4

Convert to slope intercept form

[tex]y=mx+b[/tex]

isolate the variable y

[tex]y-5=5x-20[/tex]

[tex]y=5x-20+5[/tex]

[tex]y=5x-15[/tex]

step 5

Convert to standard form

The equation in standard form is equal to

[tex]Ax+By=C[/tex]

where

A is a positive integer

B and C are integers

so

[tex]y=5x-15[/tex]

subtract y both sides

[tex]0=5x-15-y[/tex]

Adds 15 both sides

[tex]15=5x-y[/tex]

Rewrite

[tex]5x-y=15[/tex]