Question

graph the equation y = -\frac{1}{2}x; graph the equation y = -x; graph the equation y = 3x + 4; graph the equation y = x - 1

Explanation:

Step1: Identify the equation type

The equation \( y = -x \) is a linear equation in the form \( y = mx + b \), where \( m=-1 \) (slope) and \( b = 0 \) (y - intercept).

Step2: Find key points

• When \( x = 0 \), \( y=-0 = 0 \), so the y - intercept is \( (0,0) \).
• When \( x = 1 \), \( y=-1 \), so we have the point \( (1, - 1) \).
• When \( x=-1 \), \( y = 1 \), so we have the point \( (-1,1) \).

Step3: Plot the points and draw the line

Plot the points \( (0,0) \), \( (1, - 1) \), and \( (-1,1) \) on the coordinate grid (the first grid provided for \( y=-x \)). Then draw a straight line passing through these points. The line should have a negative slope (going down from left to right) and pass through the origin.

(For the other equations:

• For \( y=-\frac{1}{2}x \): It is a linear equation with \( m =-\frac{1}{2}\), \( b = 0 \). Find points like \( (0,0) \), \( (2,-1) \), \( (-2,1) \) and plot.
• For \( y = 3x + 4 \): Linear equation with \( m = 3 \), \( b = 4 \). When \( x = 0 \), \( y = 4 \) (point \( (0,4) \)); when \( x=-1 \), \( y=3\times(-1)+4 = 1 \) (point \( (-1,1) \)); when \( x = 1 \), \( y=3\times1 + 4=7 \) (point \( (1,7) \)) and plot.
• For \( y=x - 1 \): Linear equation with \( m = 1 \), \( b=-1 \). When \( x = 0 \), \( y=-1 \) (point \( (0,-1) \)); when \( x = 1 \), \( y=0 \) (point \( (1,0) \)); when \( x=-1 \), \( y=-2 \) (point \( (-1,-2) \)) and plot.)

Answer:

To graph \( y=-x \), plot the points \((0,0)\), \((1, - 1)\), \((-1,1)\) on the given grid and draw a straight line through them. (For other equations, follow similar steps of finding intercepts, additional points, and drawing the line.)