Question

1. write in point - slope form an equation of the line that passes through the point (1, 4) with slope $-\frac{3}{4}$. equation: $y - \square = \square(x - \square)$

Explanation:

Step1: Recall point - slope formula

The point - slope form of a linear equation 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.

Step2: Identify the values of \(x_1\), \(y_1\) and \(m\)

We are given that the line passes through the point \((1,4)\), so \(x_1 = 1\) and \(y_1=4\). The slope of the line \(m=-\frac{3}{4}\).

Step3: Substitute the values into the point - slope formula

Substitute \(x_1 = 1\), \(y_1 = 4\) and \(m=-\frac{3}{4}\) into the formula \(y - y_1=m(x - x_1)\). We get \(y - 4=-\frac{3}{4}(x - 1)\).

Answer:

\(y - 4=-\frac{3}{4}(x - 1)\) (So the first box is \(4\), the second box is \(-\frac{3}{4}\), and the third box is \(1\))