Question

graph the following lines given the equation in slope - intercept form
$y = 3x - 1$
$y = \frac{1}{2}x + 4$
$y = -2x + 2$
$y = -\frac{1}{3}x - 3$
$x = 1$
$y = -4$

Explanation:

For \( y = 3x - 1 \)

Step1: Identify slope and intercept

Slope \( m = 3 \), y - intercept \( b=-1 \). Plot the y - intercept \((0, - 1)\).

Step2: Use slope to find next point

Slope \( m=\frac{3}{1}\), from \((0,-1)\), move up 3 units and right 1 unit to get \((1,2)\). Draw a line through \((0, - 1)\) and \((1,2)\).

For \( y=\frac{1}{2}x + 4\)

Step1: Identify slope and intercept

Slope \( m=\frac{1}{2}\), y - intercept \( b = 4\). Plot the y - intercept \((0,4)\).

Step2: Use slope to find next point

From \((0,4)\), move up 1 unit and right 2 units to get \((2,5)\). Draw a line through \((0,4)\) and \((2,5)\).

For \( y=-2x + 2\)

Step1: Identify slope and intercept

Slope \( m=-2=\frac{-2}{1}\), y - intercept \( b = 2\). Plot the y - intercept \((0,2)\).

Step2: Use slope to find next point

From \((0,2)\), move down 2 units and right 1 unit to get \((1,0)\). Draw a line through \((0,2)\) and \((1,0)\).

For \( y =-\frac{1}{3}x-3\)

Answer:

Step1: Recognize the line type

\( y=-4\) is a horizontal line. All points on this line have a y - coordinate of - 4. Plot points like \((0,-4)\), \((1,-4)\), \((-1,-4)\) and draw a horizontal line through them.

(Note: Since the problem is about graphing linear equations, the above steps describe how to graph each line. If you need a more visual representation, you can use the grid provided to plot the points as described and draw the lines.)