Write the slope intercept form equation of line that passes through points (2,8) and (-4,-1)
The slope-intercept form of a linear equation is y = mx + b, where m represents the slope and b represents the y-intercept.
To find the slope, we use the formula:
m = (y2 - y1) / (x2 - x1)
Using the coordinates (2,8) and (-4,-1), we have:
m = (-1 - 8) / (-4 - 2)
m = -9 / -6
m = 3/2
Now that we have the slope m = 3/2, we can substitute it into the equation y = mx + b, using one of the given points (2,8):
8 = (3/2)(2) + b
Multiplying 3/2 and 2:
8 = 3 + b
Subtracting 3 from both sides:
5 = b
Therefore, the equation of the line that passes through the points (2,8) and (-4,-1) is:
y = (3/2)x + 5
To find the slope-intercept form equation of a line, we need to find the slope and the y-intercept.
The slope can be found using the formula:
m = (y2 - y1) / (x2 - x1)
For the given points (2,8) and (-4,-1), let's use (x1, y1) = (2,8) and (x2, y2) = (-4,-1).
m = (-1 - 8) / (-4 - 2)
m = (-9) / (-6)
m = 3/2
Now, we can substitute the slope and one of the points into the slope-intercept form equation, which is:
y = mx + b
Using the point (2,8), we have:
8 = (3/2)(2) + b
8 = 3 + b
To solve for b, we subtract 3 from both sides:
8 - 3 = b
5 = b
So the y-intercept is b = 5.
The slope-intercept form equation is y = (3/2)x + 5.
To find the slope-intercept form equation of a line, we need two pieces of information: the slope of the line and the y-intercept.
First, we need to find the slope (m) of the line using the given points (2, 8) and (-4, -1). The slope (m) can be calculated using the formula:
m = (y₂ - y₁) / (x₂ - x₁)
So, substituting the values of the given points, we have:
m = (-1 - 8) / (-4 - 2) = -9 / -6 = 3/2
Now that we have the slope, we can use either of the given points to find the y-intercept.
Let's use the point (2, 8).
The equation for a line in slope-intercept form (y = mx + b) tells us that the y-coordinate (8) is equal to the slope (3/2) multiplied by the x-coordinate (2), plus the y-intercept (b). We can substitute the values we have to solve for the y-intercept (b):
8 = (3/2)(2) + b
8 = 3 + b
b = 8 - 3
b = 5
Therefore, the y-intercept (b) is 5.
Now that we have the slope (m = 3/2) and the y-intercept (b = 5), we can write the equation of the line in slope-intercept form:
y = (3/2)x + 5
So, the slope-intercept form equation of the line passing through the points (2, 8) and (-4, -1) is y = (3/2)x + 5.