Question

graph this line using the slope and y-intercept: y = (7/4)x - 10 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 \(y=\frac{7}{4}x - 10\), the y - intercept \(b=- 10\). So the line crosses the y - axis at the point \((0,-10)\).

Step2: Identify slope

The slope \(m = \frac{7}{4}\), which can be written as \(\frac{\text{rise}}{\text{run}}=\frac{7}{4}\). This means from the y - intercept \((0,-10)\), we can move up 7 units and then move to the right 4 units to get another point on the line. Starting at \((0,-10)\), moving up 7 units gives \(y=-10 + 7=-3\) and moving right 4 units gives \(x = 0+4 = 4\). So another point on the line is \((4,-3)\). We can also move down 7 units and left 4 units from the y - intercept: \(y=-10-7=-17\) and \(x = 0 - 4=-4\), giving the point \((-4,-17)\) (though this point may be outside the visible grid, the two points \((0,-10)\) and \((4,-3)\) can be used to draw the line).

Answer:

To graph the line \(y=\frac{7}{4}x - 10\):

1. Plot the y - intercept at \((0,-10)\).
2. Use the slope \(\frac{7}{4}\) to find another point: from \((0,-10)\), move up 7 units and right 4 units to get \((4,-3)\).
3. Draw a straight line through the points \((0,-10)\) and \((4,-3)\) (and extend it as needed).