Write an equation in slope-intercept form for the line that satisfies each set of conditions, That Passes through (5, -2), parallel to the graph of x+2y=8
2 y = -x + 8
y = -(1/2) x + 4
so slope = -1/2
-2 = -(1/2) 5 + b
-2 = -2.5 + b
b = .5 = 1/2
so
y = -(1/2) x + 1/2
2 y + x = 1
sorry, slope intercept form is
y = -(1/2) x + 1/2
the new equation will differ from the old equation only in the constant
so new: x+2y = c , but (5,-2) is on it, so
5-4 = c = 1
x + 2y = 1
To write an equation in slope-intercept form for a line that is parallel to a given line, we need to find the slope of the given line first.
The equation of the given line, x + 2y = 8, can be rearranged into slope-intercept form (y = mx + b) by isolating y:
x + 2y = 8
2y = -x + 8
y = (-1/2)x + 4
From this equation, we can see that the slope of the given line is -1/2.
Since a line parallel to another line has the same slope, the line we are trying to find will also have a slope of -1/2.
Now we can use the point-slope form (y - y1 = m(x - x1)) to find the equation of the line passing through the point (5, -2):
y - (-2) = (-1/2)(x - 5)
y + 2 = (-1/2)x + 5/2
y = (-1/2)x + 5/2 - 2
y = (-1/2)x + 5/2 - 4/2
y = (-1/2)x + 1/2
Therefore, the equation in slope-intercept form for the line that passes through (5, -2) and is parallel to the graph of x + 2y = 8 is y = (-1/2)x + 1/2.