Question

write an equation of the line from the graph

Explanation:

First Graph (Top - Left)

Step1: Identify two points

From the graph, we can see that the line passes through \((0, -3)\) (y - intercept) and \((2, -1)\) (we can also use other points, but these are clear).

Step2: Calculate the slope \(m\)

The formula for slope is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1,y_1)=(0, - 3)\) and \((x_2,y_2)=(2, - 1)\). Then \(m=\frac{-1-(-3)}{2 - 0}=\frac{-1 + 3}{2}=\frac{2}{2}=1\).

Step3: Write the equation in slope - intercept form \(y=mx + b\)

We know that \(m = 1\) and \(b=-3\) (since the line crosses the y - axis at \((0,-3)\)). So the equation is \(y=x - 3\).

Second Graph (Top - Right)

Step1: Identify two points

The line passes through \((0,1)\) (y - intercept) and \((4,2)\) (we can also use \((-4,0)\) and \((0,1)\)). Let's use \((x_1,y_1)=(-4,0)\) and \((x_2,y_2)=(0,1)\).

Step2: Calculate the slope \(m\)

Using the slope formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\), we have \(m=\frac{1-0}{0-(-4)}=\frac{1}{4}\).

Step3: Write the equation in slope - intercept form \(y = mx + b\)

We know that \(b = 1\) (y - intercept) and \(m=\frac{1}{4}\). So the equation is \(y=\frac{1}{4}x + 1\).

Third Graph (Bottom - Left)

Step1: Identify the type of line

This is a vertical line. A vertical line has an undefined slope and its equation is of the form \(x = a\), where \(a\) is the x - coordinate of any point on the line.

Step2: Determine the value of \(a\)

Looking at the graph, the line passes through \(x=-5\) (since for all points on the line, the x - coordinate is \(-5\)). So the equation is \(x=-5\).

Fourth Graph (Bottom - Right)

Answer:

• First Graph: \(y = x-3\)
• Second Graph: \(y=\frac{1}{4}x + 1\)
• Third Graph: \(x=-5\)
• Fourth Graph: \(y=-5x + 16\)