Write the equation of each line using the given information.
the points (-4,1) and (2,4) both lie on the line.
m=-1 and the point (2,-1) lies on the line
it has the same slope as y=5 and passes through (1,1)
m=-3 and it has a y intercept of (0,8)
I am not going to do them all for you.
the first is:
slope = (4-1)/ (2+4) = 3/6 = .5
put in a point
.5 = (y-1)/(x+4)
.5 x + 2 = y -1
y = .5 x + 3
2 y = x + 6
============ the end
check
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other point (2,4)
2 ? = 2+6
2 ? = 8
? = 4 sure enough
by the way
it has the same slope as y=5 and passes through (1,1)
trick, slope is zero, horizontal line y = 1
To write the equation of a line, we can use the point-slope formula or the slope-intercept form.
1. The points (-4,1) and (2,4) lie on the line.
Using the point-slope formula:
First, find the slope (m):
m = (y2 - y1) / (x2 - x1)
m = (4 - 1) / (2 - (-4))
m = 3 / 6
m = 1/2
Now, pick one of the given points (let's use (-4,1)) and substitute into the point-slope formula:
y - y1 = m(x - x1)
y - 1 = (1/2)(x - (-4))
y - 1 = (1/2)(x + 4)
2y - 2 = x + 4
2y = x + 6
The equation of the line is: y = (1/2)x + 3.
2. The slope is -1 and the point (2,-1) lies on the line.
Using the point-slope formula:
Using the given slope, m = -1, and point (2,-1):
y - y1 = m(x - x1)
y - (-1) = -1(x - 2)
y + 1 = -x + 2
y = -x + 1
The equation of the line is: y = -x + 1.
3. The line has the same slope as y = 5 and passes through (1,1).
Given that the line has the same slope as y = 5, we have m = 0.
Using the point-slope formula, substitute the slope and point (1,1):
y - y1 = m(x - x1)
y - 1 = 0(x - 1)
y - 1 = 0
y = 1
The equation of the line is: y = 1.
4. The slope is -3, and it has a y-intercept of (0,8).
Using the slope-intercept form, y = mx + b, substitute the slope m = -3 and the y-intercept b = 8:
y = -3x + 8
The equation of the line is: y = -3x + 8.