Question

5x + 7y = -28

Explanation:

Step1: Rewrite in slope - intercept form

To graph the line \(5x + 7y=-28\), we first rewrite it in the slope - intercept form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept.
Start with \(5x+7y=-28\). Subtract \(5x\) from both sides: \(7y=-5x - 28\). Then divide each term by 7: \(y=-\frac{5}{7}x-4\).

Step2: Find the y - intercept

The y - intercept \(b=-4\). So the line crosses the y - axis at the point \((0, - 4)\). Plot this point on the coordinate plane.

Step3: Use the slope to find another point

The slope \(m =-\frac{5}{7}\). The slope is \(\frac{\text{rise}}{\text{run}}\), so from the point \((0,-4)\), we can go down 5 units (because the numerator of the slope is - 5, which means a negative rise) and then to the right 7 units (because the denominator of the slope is 7, positive run) to get the point \((0 + 7,-4-5)=(7,-9)\), or we can go up 5 units and to the left 7 units to get the point \((0 - 7,-4 + 5)=(-7,1)\).

Step4: Draw the line

Connect the points (for example, \((0,-4)\) and \((-7,1)\) or \((0,-4)\) and \((7,-9)\)) with a straight line to graph the equation \(5x + 7y=-28\).

Answer:

The line is graphed by first finding the y - intercept at \((0,-4)\) and then using the slope \(-\frac{5}{7}\) to find another point and drawing a straight line through the two points. (If the question was to graph the line, this is the process. If there was a specific part like finding intercepts:
To find the x - intercept, set \(y = 0\) in \(5x+7y=-28\), then \(5x=-28\), \(x =-\frac{28}{5}=-5.6\), so the x - intercept is \((-5.6,0)\) and the y - intercept is \((0,-4)\).)