For this case we have that by definition, the equation of a line of the slope-intersection form is given by:
[tex]y = mx + b[/tex]
Where:
m: It's the slope
b: It is the cutoff point with the y axis
By definition, if two lines are perpendicular then the product of their slopes is -1.
We have the following line:
[tex]y = 2x-6[/tex]
Then[tex]m_ {1} = 2[/tex]
The slope of a perpendicular line will be:
[tex]m_ {1} * m_ {2} = - 1\\m_ {2} = \frac {-1} {m_ {1}}\\m_ {2} = - \frac {1} {2}[/tex]
Thus, the equation of the line will be:
[tex]y = - \frac {1} {2} x + b[/tex]
We substitute the given point and find "b":
[tex]-3 = - \frac {1} {2} (0) + b\\-3 = b[/tex]
Finally the equation is:
[tex]y = - \frac {1} {2} x-3[/tex]
Answer:
[tex]y = - \frac {1} {2} x-3[/tex]
Answer:
[tex]y=-\frac{1}{2}x -3[/tex]
Step-by-step explanation:
The slope-intercept form of the equation of a line has the following form:
[tex]y=mx + b[/tex]
Where m is the slope of the line and b is the intercept with the y axis
In this case we look for the equation of a line that is perpendicular to the line
[tex]y = 2x - 6[/tex].
By definition If we have the equation of a line of slope m then the slope of a perpendicular line will have a slope of [tex]-\frac{1}{m}[/tex]
In this case the slope of the line [tex]y = 2x - 6[/tex] is [tex]m=2[/tex]:
Then the slope of the line sought is: [tex]m=-\frac{1}{2}[/tex]
The intercept with the y axis is:
If we know a point [tex](x_1, y_1)[/tex] belonging to the searched line, then the constant b is:
[tex]b=y_1-mx_1[/tex] in this case the poin is: (0,-3)
Then:
[tex]b= -3 -(\frac{1}{2})(0)\\\\b=-3[/tex]
finally the equation of the line is:
[tex]y=-\frac{1}{2}x-3[/tex]
