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i. Find an equation of the line that passes through the point (2, 4) and is perpendicular to the line 3x + 4y -22=0.
Point (x, y)=(2,4)
Rearrange above equation
Compare above equation with the equation of line slope-intercept form
m=-3/4 and b=11/2
Slope of the given line m = -3/4 and y-intercept = b = 11/2
Since required line is perpendicular, the multiplication of the slopes of both lines result in (-1), therefore the slope of the required line will be (4/3)
Now we have a point (2,4) and slope (4/3) of the required required line we can easily find the required line put these values in the equation of slope-intercept form to find the y-intercept of the required line
y-intercept of the required line =b=4/3
Put the values of ‘m’ and ‘b’ in equation of the line slope-intercept form
Above equation is the required equation of the line in slope-intercept form.
ii. Find an equation of the line passing through (-5, -4) and parallel to the line passing through(-3, 2) and (6, 8).
Points (−3,2) and (6,8)
Use point-slope Equation
Equation of the line Slope-intercept form
Put the value of any one point and slope in above equation
m=2/3, Point (-3,2)
m=2/3, Point (6,8)
Now again put the value of b and m in Equation of the Slope-intercept Form
Above equation is the Equation of the line passing through (-3,2) and (6,8)
Since the lines are paralallel their slops will be same so slope of the required line is 2/3 and it is passing through the point (-5,-4)
m=2/3, Point (-5,-4)
Put the above values in Equation of the line Slope-intercept form
y-intercept of the requaired line b=-2/3
Put m=2/3 and b=-2/3 in the Equation of the line Slope-intercept form
Above equation is the requried equation of the line.
Line passing through (-3, 2) and (6, 8)
Line passing through (-5, -4)