Question

graph this line using the slope and y-intercept: y = 7x + 2 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 \(y=7x + 2\), \(b = 2\). So the y - intercept is the point \((0,2)\). We plot this point on the graph (on the y - axis, at \(y = 2\) when \(x = 0\)).

Step2: Identify slope

The slope \(m\) in \(y=mx + b\) is 7. The slope is \(\frac{\text{rise}}{\text{run}}\), so \(m=\frac{7}{1}\). This means from the y - intercept \((0,2)\), we move up 7 units (since rise is positive) and 1 unit to the right (run is positive). Moving up 7 from \(y = 2\) gives \(y=2 + 7=9\), and moving right 1 from \(x = 0\) gives \(x = 1\). So the next point is \((1,9)\). We can also move down 7 and left 1 from the y - intercept: \(y=2-7=- 5\), \(x = 0 - 1=-1\), giving the point \((-1,-5)\) (though for the given graph with y - axis up to 10, \((1,9)\) is more visible).

Step3: Draw the line

After plotting the y - intercept \((0,2)\) and using the slope to find another point (like \((1,9)\) or \((-1,-5)\)), we draw a straight line passing through these points.

(Note: Since the problem is about graphing, the key steps are identifying the y - intercept, using the slope to find another point, and then drawing the line. The actual graphing would involve marking the points \((0,2)\) and \((1,9)\) (or other points from the slope) on the given grid and drawing a line through them.)

Answer:

To graph \(y = 7x+2\):

1. Plot the y - intercept \((0,2)\) (where the line crosses the y - axis).
2. Use the slope \(m = 7=\frac{7}{1}\): from \((0,2)\), move up 7 units and right 1 unit to get the point \((1,9)\) (or down 7 units and left 1 unit to get \((-1,-5)\)).
3. Draw a straight line through the plotted points.