the line passing through point (-3,2) with slope -5/4
To find the equation of a line passing through a given point with a given slope, we can use the point-slope form of a linear equation.
The point-slope form is given by the equation:
y - y₁ = m(x - x₁)
Where (x₁, y₁) is the given point and m is the slope.
In this case, the given point is (-3,2) and the slope is -5/4.
Substituting these values into the point-slope form, we get:
y - 2 = (-5/4)(x - (-3))
Simplifying the equation, we have:
y - 2 = (-5/4)(x + 3)
Expanding the expression on the right side, we have:
y - 2 = (-5/4)x - (5/4)(3)
Simplifying further, we get:
y - 2 = (-5/4)x - (15/4)
To isolate the y variable, we add 2 to both sides of the equation:
y = (-5/4)x - (15/4) + 2
Combining like terms, we have:
y = (-5/4)x - (15/4) + (8/4)
Simplifying the fractions, we get:
y = (-5/4)x - (7/4)
Therefore, the equation of the line passing through the point (-3,2) with a slope of -5/4 is y = (-5/4)x - (7/4).