Find the equation for the line that passes through the points ((5/8),(15/32))and((1/3),(1/4))
Give your answer in point-slope form. You do not need to simplify.
Search on Google: point-slope form calculator
thanks!
Don't let the fractions scare you ....
slope = (15/32 - 1/4)/(5/8 - 1/3)
= (15/32 - 8/32)/(15/24 - 8/24)
= (7/32) / (7/24)
= (7/32)(24/7)
= 3/4
so y - 15/32 = (3/4)(x - 5/8)
y - 15/32 = (3/4)x - 15/32
times 32
32y - 15 = 24x - 15
24x - 32y = 0
3x - 4y = 0
To find the equation of a line that passes 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) is a point on the line and m is the slope of the line.
First, let's find the slope (m) of the line using the given points ((5/8), (15/32)) and ((1/3), (1/4)).
The slope of a line passing through two points (x₁, y₁) and (x₂, y₂) is given by the formula:
m = (y₂ - y₁)/(x₂ - x₁)
Substituting the given values:
m = ((1/4) - (15/32))/((1/3) - (5/8))
To simplify this fraction, we need to find a common denominator:
m = ((1/4) - (15/32))/((8/24) - (15/24))
m = ((8/32) - (15/32))/((8 - 15)/24)
m = (-7/32)/(-7/24)
Now, dividing by a fraction can be simplified by multiplying by its reciprocal, so the expression becomes:
m = (-7/32) * (24/(-7))
m = 3/8
Now that we have the slope (m), we can pick one of the given points, say ((5/8), (15/32)), and plug them along with the slope into the point-slope form:
y - (15/32) = (3/8)(x - (5/8))
Simplifying the equation:
y - (15/32) = (3/8)x - (15/64)
This is the equation in point-slope form for the line passing through the points ((5/8), (15/32)) and ((1/3), (1/4)).