Question

problem 6.3: write an equation for this line? y = _ x + _ points (-5,4) and (4,4) on a graph.

Explanation:

Step1: Find the slope

The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \). For points \((-5, 4)\) and \((4, 4)\), we have \( y_1 = 4 \), \( y_2 = 4 \), \( x_1=-5 \), \( x_2 = 4 \). So \( m=\frac{4 - 4}{4 - (-5)}=\frac{0}{9}=0 \).

Step2: Use slope - intercept form

The slope - intercept form of a line is \( y=mx + b \), where \( m \) is the slope and \( b \) is the y - intercept. Since \( m = 0 \), the equation becomes \( y=0x + b \). We can use one of the points, say \((-5,4)\), to find \( b \). Substitute \( x=-5 \) and \( y = 4 \) into \( y=0x + b \), we get \( 4=0\times(-5)+b \), so \( b = 4 \).

Answer:

\( y = 0x+4 \) (or simply \( y = 4 \))