The line 2y+x=1is perpendicular to a line l.linel passes through points (2_1) determine the equation of l lnthe form y=mx+c
To find the equation of line l in the form y = mx + c, we first need to determine the slope of line l.
We are given that line 2y + x = 1 is perpendicular to line l. Recall that two lines are perpendicular to each other if and only if the product of their slopes is equal to -1. The equation 2y + x = 1 can be rearranged into slope-intercept form:
2y + x = 1
2y = -x + 1
y = -1/2x + 1/2
Comparing this equation to y = mx + c, we see that the slope of line 2y + x = 1 is m = -1/2. Since line l is perpendicular to this line, the slope of line l will be the negative reciprocal of -1/2.
The negative reciprocal of -1/2 is 2/1, or simply 2. Therefore, the slope of line l is m = 2.
We are also given that line l passes through the points (2, 1). Let's use the point-slope form of a linear equation to write the equation of line l:
y - y1 = m(x - x1)
where (x1, y1) is the given point on line l.
Using the point (2, 1), we have:
y - 1 = 2(x - 2)
y - 1 = 2x - 4
y = 2x - 3
Therefore, the equation of line l in the form y = mx + c is y = 2x - 3.