Write the point-slope form of the equation of the line through (-1,4) and (-4,2)
The point-slope form of the equation of a line is given by y - y₁ = m(x - x₁), where (x₁, y₁) is a point on the line, and m is the slope of the line.
To find the slope, we can use the formula m = (y₂ - y₁)/(x₂ - x₁) where (x₁, y₁) and (x₂, y₂) are the coordinates of the two given points.
Using (-1, 4) and (-4, 2) as the two points, the slope is:
m = (2 - 4)/(-4 - (-1))
= -2/(-4 + 1)
= -2/-3
= 2/3
Now that we have the slope, we can pick one of the given points, say (-1, 4), to substitute into the point-slope form equation.
x₁ = -1
y₁ = 4
m = 2/3
Therefore, the equation of the line is:
y - 4 = (2/3)(x - (-1))
Simplifying:
y - 4 = (2/3)(x + 1)
Thus, the point-slope form of the equation of the line passing through (-1, 4) and (-4, 2) is y - 4 = (2/3)(x + 1).
To find the point-slope form of the equation of a line, we need to determine the slope of the line and one point on the line.
1. Calculate the slope using the formula: slope (m) = (y2 - y1) / (x2 - x1)
Given points: (-1, 4) and (-4, 2)
Using the formula: m = (2 - 4) / (-4 - (-1)) = -2 / -3 = 2/3
2. Choose one of the points. Let's use (-1, 4) for this example.
3. Now we can write the point-slope form of the equation of the line using the slope (m) and the chosen point (x1, y1):
y - y1 = m(x - x1)
Plugging in the values:
y - 4 = (2/3)(x - (-1))
Simplifying:
y - 4 = (2/3)(x + 1)
Therefore, the point-slope form of the equation of the line through (-1, 4) and (-4, 2) is y - 4 = (2/3)(x + 1).
To find the equation of the line through two given points, we can use the point-slope form of a linear equation. The point-slope form is given as:
y - y1 = m(x - x1)
Where (x1, y1) represents one of the given points on the line, and m is the slope of the line.
Step 1: Find the slope (m) of the line
The slope is calculated using the formula:
m = (y2 - y1) / (x2 - x1)
Given points: (-1,4) and (-4,2)
Using the formula:
m = (2 - 4) / (-4 - (-1))
m = -2 / -3
m = 2/3
Step 2: Choose one of the given points
Let's choose (-1, 4) as (x1, y1).
Step 3: Plug in the values into the point-slope equation
Now, we can substitute the values into the point-slope equation:
y - y1 = m(x - x1)
y - 4 = (2/3)(x - (-1))
y - 4 = (2/3)(x + 1)
This is the point-slope form of the equation of the line through (-1,4) and (-4,2).