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]
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]