write an equation for the line that is parallel to the given line and that passes through the given point y=1/2x-8; (-6,-17)
Y=1/2x-14
you know m is 1/2
y=mx+b Put in the x,y point, and solve for b, and you have the equations
To find the equation of a line that is parallel to the given line y = (1/2)x - 8 and passes through the point (-6, -17), we need to use the point-slope form of a linear equation.
The given line has a slope of 1/2, which means any line parallel to it will also have a slope of 1/2.
Using the point-slope form, we can write the equation as:
y - y1 = m(x - x1)
Where (x1, y1) is the given point (-6, -17).
Substituting the values into the equation:
y - (-17) = (1/2)(x - (-6))
Simplifying,
y + 17 = (1/2)(x + 6)
Expanding,
y + 17 = (1/2)x + 3
Subtracting 17 from both sides,
y = (1/2)x + 3 - 17
y = (1/2)x - 14
So, the equation of the line that is parallel to y = (1/2)x - 8 and passes through (-6, -17) is y = (1/2)x - 14.
To find an equation for a line that is parallel to a given line and passes through a specific point, you can use the slope-intercept form of a line (y = mx + b), where "m" represents the slope and "b" represents the y-intercept.
Given line: y = (1/2)x - 8
To determine the slope of the given line, we can see that the coefficient of "x" is 1/2. Since parallel lines have the same slope, our desired line will also have a slope of 1/2.
Now, substitute the coordinates of the given point (-6, -17) into the slope-intercept form and solve for the y-intercept (b):
-17 = (1/2)(-6) + b
-17 = -3 + b
b = -17 + 3
b = -14
So, the equation for the line parallel to y = (1/2)x - 8 and passing through the point (-6, -17) is:
y = (1/2)x - 14