Find the equation of the line that passes through (−3, 2) and the intersection of the lines x+2y=0 and 3x+y+5=0.
For the intersection, I got (-2,1) and for the equation i got y=x+3. but apparently those aren't the answer. Could you provide a way to solve, but not the complete anser for the question, but i might ask for one after i have tried the suggestion
ok, you have the intersection (-2,1)
now the line
slope=(changeY)/(changex)=(1-2)/(-2+3)=-1
y= mx+b
1= (-1)(-2)+b
b=1-2=-1
y=-x-1 check that.
it worked thanks for the help
you have a point and a slope, so use the point-slope form of the line:
y-2 = -1(x+3)
Thank you for that suggestion!!
To find the equation of the line passing through two given points, we need to find the slope of the line and a point on the line.
First, let's find the intersection point of the two given lines, x+2y=0 and 3x+y+5=0. To do this, we can solve the two equations simultaneously.
We have:
x + 2y = 0 ---(1)
3x + y + 5 = 0 ---(2)
To solve for x and y, we can use the method of substitution. From equation (1), we can rearrange it to find x:
x = -2y ---(3)
Now, substitute equation (3) into equation (2):
3(-2y) + y + 5 = 0
-6y + y + 5 = 0
-5y + 5 = 0
-5y = -5
y = 1
Now substitute the value of y back into equation (3) to find x:
x = -2(1)
x = -2
Hence, the intersection point is (-2, 1).
Next, we need to determine the slope of the line passing through (-3, 2) and (-2, 1). The slope of a line can be found using the formula:
slope = (y2 - y1) / (x2 - x1)
Let's substitute the coordinates into the formula:
slope = (1 - 2) / (-2 - (-3))
slope = (-1) / (1)
slope = -1
Now that we have the slope (-1) and a point on the line (-2, 1), we can use the point-slope form of a line to find the equation. The point-slope form is:
y - y1 = m(x - x1)
Substituting the values into the equation:
y - 1 = -1(x - (-2))
y - 1 = -1(x + 2)
y - 1 = -x - 2
y = -x - 1
Hence, the equation of the line passing through (-3, 2) and the intersection of the lines x + 2y = 0 and 3x + y + 5 = 0 is y = -x - 1.