Question

graph this line using the slope and y-intercept:
y = 4x - 6
click to select points on the graph.

Explanation:

Step1: Identify y-intercept

The equation is in slope - intercept form \(y = mx + b\), where \(b\) is the y - intercept. For \(y=4x - 6\), \(b=-6\), so the y - intercept is \((0,-6)\).

Step2: Identify slope

The slope \(m = 4=\frac{4}{1}\), which means for every 1 unit we move to the right (increase in \(x\) by 1), we move up 4 units (increase in \(y\) by 4).

Step3: Plot points

• Start by plotting the y - intercept \((0,-6)\).
• From \((0,-6)\), use the slope. Move 1 unit to the right (to \(x = 1\)) and 4 units up (to \(y=-6 + 4=-2\)), so we get the point \((1,-2)\).
• We can also go in the opposite direction: from \((0,-6)\), move 1 unit to the left (to \(x=-1\)) and 4 units down (to \(y=-6-4 = - 10\)), getting the point \((-1,-10)\).
• Draw a straight line through these points (or more points found using the slope) to graph the line \(y = 4x-6\).

Answer:

To graph \(y = 4x-6\):

1. Plot the y - intercept \((0,-6)\) (since when \(x = 0\), \(y=-6\)).
2. Use the slope \(m = 4=\frac{4}{1}\): from \((0,-6)\), move 1 unit right and 4 units up to get \((1,-2)\), or 1 unit left and 4 units down to get \((-1,-10)\).
3. Draw a straight line through the plotted points. The line will pass through points like \((0,-6)\), \((1,-2)\), \((-1,-10)\) etc.