Question

1. graph of a line on a coordinate plane with x-axis from -8 to 8 and y-axis from -8 to 8, line passes through (0,7) and other points

Explanation:

Step1: Identify two points

From the graph, the line passes through \((0, 7)\) (y - intercept) and \((4, 6)\) (we can pick another point for slope calculation).

Step2: Calculate the slope

The slope \(m\) is given by \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Using \((x_1,y_1)=(0,7)\) and \((x_2,y_2)=(4,6)\), we get \(m=\frac{6 - 7}{4 - 0}=\frac{- 1}{4}=-\frac{1}{4}\).

Step3: Write the equation

Using the slope - intercept form \(y = mx + b\), where \(m =-\frac{1}{4}\) and \(b = 7\) (from the y - intercept \((0,7)\)), the equation is \(y=-\frac{1}{4}x + 7\).

Answer:

The equation of the line is \(y =-\frac{1}{4}x+7\)