Question

question
what is the equation of the line that passes through the point (4, -2) and has a slope of \\(\frac{3}{4}\\)?

Explanation:

Step1: Recall point - slope form

The point - slope form of a line is given by \(y - y_1=m(x - x_1)\), where \((x_1,y_1)\) is a point on the line and \(m\) is the slope of the line.
Here, \(x_1 = 4\), \(y_1=-2\) and \(m=\frac{3}{4}\).
Substitute these values into the point - slope formula: \(y-(-2)=\frac{3}{4}(x - 4)\)

Step2: Simplify the equation

Simplify the left - hand side: \(y + 2=\frac{3}{4}(x - 4)\)
Distribute the \(\frac{3}{4}\) on the right - hand side: \(y+2=\frac{3}{4}x-3\)
Subtract 2 from both sides to solve for \(y\): \(y=\frac{3}{4}x-3 - 2\)
Simplify the right - hand side: \(y=\frac{3}{4}x-5\)

Answer:

The equation of the line is \(y=\frac{3}{4}x - 5\) (or in standard form \(3x-4y = 20\))