Question

Using the concept of the family of lines, find the equation of a member. Show your complete solution 4. Joining the origin and the point of intersection of the lines 4x+3y=8 and x+y=1 5. Has y - intercept =−3 and perpendicular to the line 3x+5y=4 6. Passing through the point of intersection of the lines 2x−y−1=0 and 3x+2y−12=0 and passes through (−2,1).

Answer 1

To find the equation of a line using the concept of the family of lines, solve each part of the question step by step. Determine the point of intersection of two lines and use the formula for the equation. Find the slope of a line using the fact that perpendicular lines have negative reciprocal slopes and use the slope-intercept form of the equation. Use the point-slope form of the equation to find the required equation.

Step-by-step explanation:

To find the equation of a line using the concept of the family of lines, you need to determine the equation that satisfies the given condition. Let's solve each part of the question step by step:

1. To find the equation joining the origin and the point of intersection of the lines 4x+3y=8 and x+y=1, first determine the point of intersection by solving the system of equations. Then, use the formula for the equation of a line passing through two points to find the required equation.
2. To find the equation of a line with a y-intercept of -3 and perpendicular to the line 3x+5y=4, determine the slope of the given line and then use the fact that perpendicular lines have negative reciprocal slopes to find the slope of the desired line. Finally, use the slope-intercept form of the equation of a line to find the equation.
3. To find the equation passing through the point of intersection of the lines 2x-y-1=0 and 3x+2y-12=0 and passing through (-2,1), first determine the point of intersection by solving the system of equations. Then use the point-slope form of the equation of a line to find the required equation.

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