A line passes through the point (3,-1) and has a slope of -2/3
To find the equation of the line that passes through the point (3, -1) and has a slope of -2/3, we will use the point-slope form of a linear equation.
The equation of a line in point-slope form is given as:
y - y1 = m(x - x1)
Where:
(x1, y1) are the coordinates of a point on the line
m is the slope of the line
Substituting the given values into the equation, we have:
y - (-1) = -2/3(x - 3)
Multiplying through by 3 to eliminate the fraction, we have:
3(y + 1) = -2(x - 3)
Expanding the equation, we have:
3y + 3 = -2x + 6
Subtracting 3 from both sides, we have:
3y = -2x + 3
Dividing through by 3 to solve for y, we have:
y = (-2/3)x + 1
So, the equation of the line passing through the point (3, -1) with a slope of -2/3 is y = (-2/3)x + 1.