Question

graph the line.
y = x

Explanation:

Step1: Identify the slope and intercept

The equation \( y = x \) is in slope - intercept form \( y=mx + b \), where \( m = 1 \) (slope) and \( b = 0 \) (y - intercept). So the line passes through the origin \((0,0)\).

Step2: Find another point

Using the slope \( m = 1=\frac{\text{rise}}{\text{run}}=\frac{1}{1}\), from the point \((0,0)\), we move 1 unit up and 1 unit to the right to get the point \((1,1)\). We can also find other points like \((2,2)\), \((- 1,-1)\) etc.

Step3: Plot the points and draw the line

Plot the points \((0,0)\), \((1,1)\), \((2,2)\), \((-1,-1)\) on the coordinate plane and then draw a straight line passing through these points. The line should have a positive slope of 1 and pass through the origin, making a \( 45^{\circ} \) angle with both the x - axis and y - axis.

Answer:

To graph \( y = x \), plot the points \((0,0)\), \((1,1)\), \((2,2)\), \((-1,-1)\) (and others) and draw a straight line through them with a slope of 1 passing through the origin.