Question

warm-up: prove systems of two equations practice
graph the equation ( y = 3x - 1 )
use the point button to locate the y - intercept, then use the label button to label its coordinates in the format ( (x, y) ).
use the line button to graph the line, then use the label button on the line to label the slope in the format ( m = n ).

Explanation:

Step1: Find the y - intercept

The equation of the line is \(y = 3x-1\). For the y - intercept, we set \(x = 0\). Substituting \(x = 0\) into the equation \(y=3(0)-1=- 1\). So the y - intercept is the point \((0,-1)\).

Step2: Find another point

Let's choose \(x = 1\). Substitute \(x = 1\) into the equation \(y = 3(1)-1=3 - 1=2\). So we have another point \((1,2)\).

Step3: Graph the line

Plot the points \((0,-1)\) and \((1,2)\) on the coordinate plane. Then draw a straight line passing through these two points. The slope \(m\) of the line \(y=mx + b\) (where \(b\) is the y - intercept) for the equation \(y = 3x-1\) is \(m = 3\), which means for every 1 unit we move to the right along the x - axis, we move up 3 units along the y - axis.

To label the y - intercept: The y - intercept is at \((0,-1)\), so we label the point \((0,-1)\) using the label button. Then, to draw the line, we use the line button to connect the points \((0,-1)\) and \((1,2)\) (or other points on the line). After drawing the line, we can label the line with the equation \(y = 3x-1\) and note that the slope \(m = 3\).

Answer:

To graph \(y = 3x-1\):

1. Plot the y - intercept \((0,-1)\) (set \(x = 0\), \(y=-1\)).
2. Plot another point, e.g., \((1,2)\) (set \(x = 1\), \(y = 3(1)-1 = 2\)).
3. Draw a straight line through \((0,-1)\) and \((1,2)\). The slope of the line is \(3\), and the y - intercept is \(-1\).