Question

use the following graph to fill in the blanks for the slope - intercept form equation.

Explanation:

Step1: Identify two points on the line

Looking at the graph, the line passes through the origin \((0,0)\) and another point, say \((1, -1)\) (we can check the grid: from \((0,0)\), moving 1 unit right (x - direction) and 1 unit down (y - direction) gives \((1, -1)\)).

Step2: Calculate the slope (\(m\))

The formula for slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Using \((x_1,y_1)=(0,0)\) and \((x_2,y_2)=(1, -1)\), we get \(m=\frac{-1 - 0}{1 - 0}=- 1\).

Step3: Determine the y - intercept (\(b\))

The y - intercept is the value of \(y\) when \(x = 0\). Since the line passes through \((0,0)\), \(b = 0\).

Step4: Write the slope - intercept form (\(y=mx + b\))

Substituting \(m=-1\) and \(b = 0\) into \(y=mx + b\), we get \(y=-1x+0\) or \(y=-x\).

Answer:

The equation of the line in slope - intercept form is \(y=-x + 0\) (or \(y=-x\)). The slope (\(m\)) is \(-1\) and the y - intercept (\(b\)) is \(0\).