What is the equation in point slope from of the line that passes through the given points (9,1),(5,2)
Not 9th grade, but Math.
Sra
The slope is
m = (2-1)/(5-9) = -1/4
so the general equation is
y = (-x/4) + b
where b is a constant.
Evaluate b by making the line go through either point. For example
2 = (-1/4)*5 + b
b = 13/4
Therefore the final equation is
y = -x/4 + 13/4 or
y = (13-x)/4
To find the equation of a line in point-slope form, you need two things: a point on the line and the slope of the line. Let's call the given points (x₁, y₁) = (9, 1) and (x₂, y₂) = (5, 2).
Step 1: Calculate the slope (m) of the line using the formula:
m = (y₂ - y₁) / (x₂ - x₁)
Substituting the values:
m = (2 - 1) / (5 - 9)
m = 1 / (-4)
m = -1/4
Step 2: Choose one of the given points as (x₁, y₁). Let's use (9, 1).
Step 3: Write the equation in point-slope form using the values of m and (x₁, y₁):
y - y₁ = m(x - x₁)
Substituting the values:
y - 1 = (-1/4)(x - 9)
Step 4: Simplify and rearrange the equation (if necessary) to get the final form:
y - 1 = (-1/4)x + (9/4)
This is the equation in point-slope form for a line passing through the given points (9,1) and (5,2).