Final answer:
To find the standard form of the equation of a line that goes through (4,3) with a slope of -2/3, we start with the point-slope form, substitute the given values, and then rearrange to get 2x + 3y = 17.
Step-by-step explanation:
The question asks us to write the equation of a line in standard form given that the line passes through the point (4,3) and has a slope of -2/3. The standard form of a line's equation is usually expressed as Ax + By = C. To find the standard form, we will start with the point-slope form of a line's equation, which is derived from the slope formula and is represented as (y - y1) = m (x - x1), where (x1, y1) is a given point on the line and m is the slope.
Using the point (4,3) and the slope -2/3, we can plug these values into the point-slope form:
y - 3 = -2/3(x - 4)
Distributing the slope on the right side of the equation gives us:
y - 3 = -2/3x + 8/3
To get to the standard form, we will clear the fraction by multiplying every term by 3, the denominator of our fraction, which yields:
3y - 9 = -2x + 8
And then rearrange to get terms involving 'x' and 'y' on one side and the constant on the other:
2x + 3y = 8 + 9
2x + 3y = 17
So, the standard form of the line is:
2x + 3y = 17