Find the equation of a line that passes through the points (1/3, 2/5) and (–4/5, 1/2). Please put your final answer in standard form (Ax + By = C) and please make sure that there are NO fractions (or decimals) in this answer and that the “x” term is positive. Make sure to show all of your work
the slope is (1/2 - 2/5)/(-4/5 - 1/3) = -3/34
So, now you can use the point-slope form to get the equation for the line as
y = -3/34 (x - 1/3) + 2/5
You can massage that into the form you want. I assume you can get rid of the fractions.
To find the equation of a line that passes through two given points, we can use the point-slope form of a linear equation and then convert it into standard form.
First, let's find the slope of the line using the two points (x₁, y₁) = (1/3, 2/5) and (x₂, y₂) = (–4/5, 1/2):
slope (m) = (y₂ - y₁) / (x₂ - x₁)
Plugging in the values, we get:
m = (1/2 - 2/5) / (–4/5 - 1/3)
= (-1/10) / (-17/15) [finding the common denominator]
= (1/10) / (17/15)
= (1/10) * (15/17)
= 15/170
= 3/34
So, the slope (m) of the line is 3/34.
Next, we can use the point-slope formula with one of the given points (let's use (1/3, 2/5)) to find the equation in point-slope form:
y - y₁ = m(x - x₁)
y - (2/5) = (3/34)(x - 1/3)
Expanding the right side:
y - 2/5 = 3/34 * (x - 1/3)
y - 2/5 = 3/34 * (x - 1/3)
y - 2/5 = 3/34 * x - 3/34 * 1/3
y - 2/5 = 3/34 * x - 1/34
Now, let's simplify the expression:
Multiply through by the common denominator, 34:
34(y - 2/5) = 34(3/34 * x - 1/34)
34y - 2 * 34/5 = 3x - 1
Rearranging the equation:
3x - 34y = 68/5 - 2 * 34/5
3x - 34y = 68/5 - 68/5
3x - 34y = 0
Since we want the "x" term to be positive, we can multiply the entire equation by -1:
-3x + 34y = 0
Finally, let's rewrite the equation in standard form (Ax + By = C) by multiplying through by -1 to make the coefficient of "x" positive:
3x - 34y = 0
So, the equation of the line that passes through the points (1/3, 2/5) and (–4/5, 1/2) in standard form is 3x - 34y = 0.