Write the equation of the line in slope-intercept form.
(3,0) (0,-2)
To find the slope of the line, we can use the formula:
slope = (change in y) / (change in x)
Using the given points (3,0) and (0,-2):
change in y = -2 - 0 = -2
change in x = 0 - 3 = -3
slope = (-2) / (-3)
slope = 2/3
Now that we have the slope, we can use the point-slope form of a linear equation:
y - y1 = m(x - x1)
where m is the slope, and (x1, y1) is any point on the line. Let's use the point (3,0):
y - 0 = (2/3)(x - 3)
Simplifying the equation:
y = (2/3)(x - 3)
This is the equation of the line in slope-intercept form.
Write the equation of the line in slope-intercept form.
(1,-1) (0,2)
To find the equation of the line in slope-intercept form, we need to find the slope and the y-intercept.
Using the given points (1, -1) and (0, 2), we can calculate the slope using the formula:
slope = (change in y) / (change in x)
change in y = 2 - (-1) = 2 + 1 = 3
change in x = 0 - 1 = -1
slope = 3 / -1 = -3
Now that we have the slope, we can use the point-slope form of a linear equation:
y - y1 = m(x - x1)
where m is the slope and (x1, y1) is any point on the line. Let's use point (1, -1):
y - (-1) = -3(x - 1)
Simplifying the equation:
y + 1 = -3x + 3
Now, let's rearrange the equation to the slope-intercept form, which is in the form y = mx + b, where m is the slope and b is the y-intercept:
y = -3x + 3 - 1
y = -3x + 2
This is the equation of the line in slope-intercept form.
Write the equation of the line in slope-intercept form.
(1,8) (0,4)
To find the equation of the line in the slope-intercept form (y = mx + b), we need to find the slope (m) and the y-intercept (b).
Using the given points (1,8) and (0,4), we can calculate the slope using the formula:
slope (m) = (change in y) / (change in x)
Let's call the coordinates of the first point (x1, y1) = (1,8) and the coordinates of the second point (x2, y2) = (0,4):
change in y = y2 - y1 = 4 - 8 = -4
change in x = x2 - x1 = 0 - 1 = -1
slope (m) = (-4) / (-1) = 4
Now that we have the slope, we can use the point-slope form of a linear equation:
y - y1 = m(x - x1)
Substituting the values from the first point (1,8):
y - 8 = 4(x - 1)
Expanding the equation:
y - 8 = 4x - 4
To rearrange the equation to the slope-intercept form (y = mx + b), we isolate y:
y = 4x - 4 + 8
y = 4x + 4
Therefore, the equation of the line in slope-intercept form is y = 4x + 4.
To find the equation of a line in slope-intercept form (y = mx + b), we need to first determine the slope (m) and then find the y-intercept (b).
Given the two points (3,0) and (0,-2), we can find the slope using the formula:
m = (y2 - y1) / (x2 - x1)
Using (3,0) as (x1,y1) and (0,-2) as (x2,y2), the slope is:
m = (-2 - 0) / (0 - 3)
= -2 / -3
= 2/3
Now that we have the slope, we can use one of the given points to find the y-intercept (b). Let's use (3,0).
Substituting x=3, y=0, and m=2/3 into the slope-intercept form (y = mx + b):
0 = (2/3)(3) + b
0 = 2 + b
b = -2
Therefore, the equation of the line is:
y = (2/3)x - 2
To find the equation of a line in slope-intercept form (y = mx + b), we need to find the slope (m) and the y-intercept (b).
1. Start by finding the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
Let's label the coordinates as follows: (x1, y1) = (3, 0) and (x2, y2) = (0, -2).
Plugging the values into the formula, we get:
m = (-2 - 0) / (0 - 3)
= -2 / -3
= 2/3
2. Now that we have the slope (m), we can use one of the given points (3,0) to find the y-intercept (b).
We can rearrange the slope-intercept form to solve for b:
y = mx + b --> b = y - mx
Plugging in the values (x = 3, y = 0, m = 2/3), we get:
b = 0 - (2/3) * 3
= 0 - 2
= -2
3. Now that we have the slope (m = 2/3) and the y-intercept (b = -2), we can write the equation of the line in slope-intercept form:
y = (2/3)x - 2