Write in point-slope form an equation of the line through the pair of points.
(5,3) and (11,10)
The point-slope form of a linear equation is given by:
y - y1 = m(x - x1)
Where:
m is the slope of the line, and
(x1, y1) is a point on the line.
To find the slope (m), we use the formula:
m = (y2 - y1)/(x2 - x1)
Given the points (5, 3) and (11, 10), we can substitute the coordinates into the formula:
m = (10 - 3)/(11 - 5)
m = 7/6
Now that we have the slope, we can choose any of the given points to plug in to the point-slope form.
Let's choose (5, 3):
y - 3 = (7/6)(x - 5)
Simplifying the equation gives us the final answer:
y - 3 = (7/6)x - (35/6)
To write the equation of a line in point-slope form, we need the coordinates of a point on the line and the slope of the line.
Given the points (5,3) and (11,10), we can find the slope of the line using the formula:
slope (m) = (y₂ - y₁)/(x₂ - x₁)
Let's substitute the coordinates into the formula:
slope (m) = (10 - 3)/(11 - 5)
= 7/6
Now that we have the slope, let's use the point-slope form of the equation:
y - y₁ = m(x - x₁)
Using the point (5,3) and slope 7/6:
y - 3 = (7/6)(x - 5)
This is the equation of the line in point-slope form.
To write the equation of a line in point-slope form, we need to use the formula: y - y₁ = m(x - x₁), where (x₁, y₁) represents one of the given points and m represents the slope of the line.
Step 1: Find the slope.
The slope (m) can be calculated using the formula: m = (y₂ - y₁) / (x₂ - x₁), where (x₁, y₁) and (x₂, y₂) are the coordinates of the two points.
Using the given points (5,3) and (11,10):
m = (10 - 3) / (11 - 5)
m = 7 / 6
Step 2: Choose one of the points and substitute the coordinates into the equation.
Let's choose point (5,3), so x₁ = 5 and y₁ = 3.
y - 3 = (7/6)(x - 5)
Therefore, the equation of the line through the points (5,3) and (11,10) in point-slope form is y - 3 = (7/6)(x - 5).