find an equation of the line that passes through the points
(0,0),(-1,5)
and
(2,1),(0,-3)
The first one is
slope = y1-y2/x1-x2
slope = m = (0-5/0+1 = -5
y = mx + b
Then put in one of the points to calculate b.
5 = -5(-1) + b
5 = 5 + b
b = 0
So the line is
y= mx + b
y = -5x + 0 or y = -5x.
The other one is don the same way.
Check my work very carefully.
is the other problem is
y=-3x+0
The first pair is very very easy.
Remember that a line that passes through the origin must be of the form:
y = mx
since the intercept is zero. You are told that this line passes through the origin and that the point (-1, 5) satisfies the equation. You should be able to write the answerdown from there.
There are a couple of ways to do the second one. he two-point formula is
(y - y1) / (x - x1) = (y2 - y1) / (x2 -x1)
(y - 1) / (x - 2) = (-3 - 1) / (0 - 2)
(y - 1) / (x - 2) = 2
multiply across by x - 2
y -1 = 2x - 4
and you should be close enough to finish from there.
To find the equation of a line that passes through two points, we first need to determine the slope of the line.
1) Find the slope (m):
The formula to find the slope (m) between two points (x₁, y₁) and (x₂, y₂) is given by:
m = (y₂ - y₁) / (x₂ - x₁)
For the first set of points (0,0) and (-1,5), we substitute the values into the formula:
m₁ = (5 - 0) / (-1 - 0)
m₁ = 5 / -1
m₁ = -5
For the second set of points (2,1) and (0,-3), we substitute the values into the formula:
m₂ = (-3 - 1) / (0 - 2)
m₂ = -4 / -2
m₂ = 2
2) Find the y-intercept (b):
To find the y-intercept (b), we can use the equation of a line:
y = mx + b
Using one of the given points, we can substitute the values into the equation and solve for b.
For the first set of points (0,0):
0 = -5(0) + b
0 = b
For the second set of points (2,1):
1 = 2(2) + b
1 = 4 + b
b = 1 - 4
b = -3
3) Write the equation of the line:
Now that we have the slope (m) and the y-intercept (b), we can write the equation of the line using the slope-intercept form:
y = mx + b
For the first set of points (0,0) and (-1,5):
y = -5x + 0
For the second set of points (2,1) and (0,-3):
y = 2x - 3
Therefore, the equations of the lines that pass through the given sets of points are:
1) First set of points: y = -5x
2) Second set of points: y = 2x - 3