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 is the slope of the line
b: It is the cut point with the y axis
By definition, if two lines are perpendicular then the product of their slopes is -1.
If we have: [tex]y = 2x-7[/tex]
[tex]m_ {1} = 2\\2 * m 2 = - 1\\m_ {2} = - \frac {1} {2}[/tex]
Thus, the equation is of the form:
[tex]y = - \frac {1} {2} x + b[/tex]
We substitute the point:
[tex]-1 = - \frac {1} {2} (6) + b\\-1 = - \frac {1} {2} (6) + b\\-1 = -3 + b\\-1 + 3 = b\\b = 2[/tex]
Finally, the equation is:
[tex]y = - \frac {1} {2} x + 2[/tex]
Answer:
[tex]y = - \frac {1} {2} x + 2[/tex]
The equation in slope-intercept form that represents a line that passes through the point (6,−1) and is perpendicular to the line y=2x−7 is y = - 1 / 2 x +2
where
m = slope
b = y-intercept
The equation of the line passes through (6, -1) and is perpendicular to the line y = 2x - 7
For perpendicular line
m₁m₂ = -1
2m₂ = -1
m₂ = -1 / 2
Therefore,
y = - 1 /2 x + b
-1 = - 1 / 2 (6) + b
b = 2
The equation is y = - 1/ 2 x +2
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