write an equation in point slope form for the line with the given slope that contains the given point..
slope=5;(1,7) is on the line
(8,-2) and (4,-4) are on the line
y=mx+b=5x+b
put in the x,y point, solve for b.
7=5*1+b
b=2
y=5x+2
(8,-2) and (4,-4) are on the line
Find slope: m = y2 - y1/x2 - x1
-4 - (-2)/4 - 8 = -2/-4 = 1/2
m = 1/2
Use either point to find y-intercept.
y = mx + b
-4 = 1/2(4) + b
-4 = 2 + b
-4 - 2 = 2 - 2 + b
-6 = b
y = 1/2x - 6
To write the equation of a line in point-slope form, we use the formula:
y - y1 = m(x - x1),
where m represents the slope, and (x1, y1) is a point on the line.
For the first scenario, where the slope is 5 and the point (1,7) is on the line, the equation can be written as:
y - 7 = 5(x - 1).
For the second scenario, where the points (8,-2) and (4,-4) are on the line, we need to find the slope first. The formula for slope is:
m = (y2 - y1) / (x2 - x1).
Using the two points (8,-2) and (4,-4), we can find the slope:
m = (-4 - (-2)) / (4 - 8)
= (-4 + 2) / (-4)
= -2 / (-4)
= 1/2.
Now we can write the equation using the slope (1/2) and one of the given points, let's say (8,-2):
y - (-2) = 1/2(x - 8),
y + 2 = 1/2(x - 8).
Therefore, the equation of the line is y + 2 = 1/2(x - 8).
To write an equation in point-slope form, we need the slope and a point on the line. Let's start with the first line:
1. slope = 5, point (1,7) is on the line.
The point-slope form of a line is: y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line.
In this case, the slope (m) is 5, and the given point is (1,7). Plugging these values into the equation, we have:
y - 7 = 5(x - 1)
You can simplify this equation further if needed.
Now, let's move on to the second line:
2. Points (8,-2) and (4,-4) are on the line.
We need to find the slope first using the formula:
slope = (change in y) / (change in x)
Given the points (8,-2) and (4,-4), the change in y is -4 - (-2) = -4 + 2 = -2,
and the change in x is 4 - 8 = -4.
Thus, the slope is (-2) / (-4) = 1/2.
Now that we have the slope, we can choose any one of the given points. Let's use (8,-2) for this example:
Using the point-slope form with slope (m = 1/2) and point (8,-2), we have:
y - (-2) = 1/2(x - 8)
Simplifying the equation further, we get:
y + 2 = 1/2x - 4
And there you have it. These are the equations in point-slope form for the given lines. Remember to double-check your work and simplify the equations further if needed.