Question

y = \frac{2}{7}x - 6
click to select points on the graph.
(graph with x-axis from -10 to 10 and y-axis from -8 to 10, grid lines)

Explanation:

Step1: Identify the y - intercept

The equation of the line is in slope - intercept form \(y = mx + b\), where \(b\) is the y - intercept. For the equation \(y=\frac{3}{7}x - 6\), the y - intercept \(b=-6\). So the line crosses the y - axis at the point \((0,-6)\).

Step2: Find another point using the slope

The slope \(m = \frac{3}{7}\), which means for a run of 7 (change in \(x\)), the rise is 3 (change in \(y\)). Starting from the y - intercept \((0,-6)\), if we move 7 units to the right (increase \(x\) by 7) and 3 units up (increase \(y\) by 3), we get the point \((0 + 7,-6+3)=(7, - 3)\). We can also check the x - intercept by setting \(y = 0\):

$$
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But 14 is outside the given grid. So we can use the two points \((0,-6)\) and \((7,-3)\) to plot the line. To select points on the graph, we can click on \((0,-6)\) (where the line crosses the y - axis at \(y=-6\)) and \((7,-3)\) (by moving 7 units right and 3 units up from the y - intercept).

Answer:

To plot the line \(y = \frac{3}{7}x-6\), select the points \((0, - 6)\) (y - intercept) and \((7,-3)\) (using the slope \(\frac{3}{7}\)) on the graph.