Write an equation of the line that is parallel to the equation 5x – 2y = 6, that passes through (4, -2).
Thanks Dude!
To find the equation of a line that is parallel to a given line, we need to know that parallel lines have the same slope.
The given equation 5x - 2y = 6 is not in slope-intercept form (y = mx + b), so we need to rearrange it to find the slope.
Step 1: Rewrite the equation in slope-intercept form (y = mx + b):
5x - 2y = 6
-2y = -5x + 6
y = (5/2)x - 3
From this equation, we can see that the slope of the given line is 5/2.
To find the equation of a line parallel to this line, we can use the slope-intercept form (y = mx + b) and substitute the values of the given point (4, -2).
Step 2: Plug in the values of the point and the slope to the slope-intercept form:
y = mx + b
-2 = (5/2)(4) + b
Simplify the equation:
-2 = 10 + b
b = -12
Step 3: Substitute the value of b back into the equation to find the final equation:
y = (5/2)x - 12
Therefore, the equation of the line that is parallel to 5x - 2y = 6 and passes through (4, -2) is y = (5/2)x - 12.
Re-arrange for y=mx+b then look at the m value (the slope), re-write your equation with the new slope... which is 5/2 (when you re-arrange the equation). Then use
y=(5/2)x + b and sub in your ordered pair (x,y) which is (4, -2)and solve for b : ) Then re-write the equation with that b and the 5/2 slope.
5x-2y = 6.
m = -A/B = -5/-2 = 5/2 = Slope.
(4,-2)
Y = mx + b.
-2 = (5/2)4 + b,
b = -12.
Eq.: Y = (5/2)x - 12.