find the equation of the line joining the origin to the point of intersection 4x+3y=8 and x+y=1
The lines intersect at (5,-4)
y = -4/5 x
I need the solving
To find the equation of the line joining the origin to the point of intersection of the two given lines, you will need to follow these steps:
Step 1: Find the point of intersection.
- Solve the system of equations formed by the given equations:
4x + 3y = 8
x + y = 1
You can solve this system of equations either by substitution or by elimination. Let's use the elimination method:
- Multiply the second equation by 4 to make the x coefficients cancel each other out:
4(x + y) = 4(1)
4x + 4y = 4
- Now subtract this new equation from the first equation to eliminate the x variable:
(4x + 3y) - (4x + 4y) = 8 - 4
4x - 4x + 3y - 4y = 4
-y = 4
- Divide both sides of the equation by -1 to solve for y:
y = -4
- Substitute the value of y = -4 into either of the original equations to solve for x:
x + (-4) = 1
x - 4 = 1
x = 1 + 4
x = 5
Therefore, the point of intersection of the two lines is (5, -4).
Step 2: Find the slope of the line joining the origin and the point of intersection.
To find the slope, we use the formula:
slope = (y2 - y1) / (x2 - x1)
Given that the coordinates of the origin are (0, 0) and the coordinates of the point of intersection are (5, -4), we substitute the values into the formula:
slope = (-4 - 0) / (5 - 0)
slope = -4/5
Step 3: Write the equation of the line.
The equation of a line can be written in slope-intercept form as:
y = mx + b
where m is the slope and b is the y-intercept.
Since the line passes through the origin, its y-intercept is 0. Thus, the equation becomes:
y = (-4/5)x + 0
Simplifying, the equation is:
y = (-4/5)x
Therefore, the equation of the line joining the origin to the point of intersection of the given lines is y = (-4/5)x.