Find an equation of the line that satisfies the given conditions
Through (-5,1) perpendicular to the line y=-1/2x+6
Since the given line has a slope of -1/2, the perpendicular line will have a slope of 2 (since the product of the slopes of perpendicular lines is -1).
We can use the point-slope form of a linear equation to find the equation of the line:
y - y1 = m(x - x1)
Using the point (-5,1) and the slope m = 2:
y - 1 = 2(x - (-5))
y - 1 = 2(x + 5)
y - 1 = 2x + 10
Finally, rearranging the equation:
2x - y = -9
Therefore, the equation of the line that satisfies the given conditions is 2x - y = -9.
To find an equation of a line that is perpendicular to another line, we need to determine the slope of the given line and then find the negative reciprocal of that slope.
Given the equation of the line y = (-1/2)x + 6, we can see that the slope of this line is -1/2.
The negative reciprocal of -1/2 is 2/1, also known as 2.
Now we have the slope, and we can use the point-slope form of a linear equation to find the equation of the line that passes through the point (-5,1) with a slope of 2. The point-slope form is given by:
y - y₁ = m(x - x₁)
where (x₁, y₁) is the given point and m is the slope.
Plugging in the values (-5, 1) and m = 2, we have:
y - 1 = 2(x - (-5))
Simplifying further:
y - 1 = 2(x + 5)
Expanding the brackets:
y - 1 = 2x + 10
Finally, rearranging the equation:
2x - y = -11
Therefore, the equation of the line that passes through (-5,1) and is perpendicular to the line y = (-1/2)x + 6 is 2x - y = -11.