Question

(7) 5x - 7y = 7

Explanation:

Step1: Rewrite in slope - intercept form

We start with the equation \(5x - 7y=7\). We want to solve for \(y\) to get it in the form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept.
First, subtract \(5x\) from both sides: \(- 7y=-5x + 7\).
Then, divide each term by \(-7\): \(y=\frac{5}{7}x - 1\).

Step2: Find the y - intercept

The y - intercept \(b=- 1\). So the line crosses the y - axis at the point \((0,-1)\).

Step3: Find another point using the slope

The slope \(m = \frac{5}{7}\), which means for every 7 units we move to the right (increase in \(x\) by 7), we move up 5 units (increase in \(y\) by 5). Starting from \((0,-1)\), if we move \(x = 7\), then \(y=-1 + 5=4\). So another point on the line is \((7,4)\). But since our graph only goes up to \(x = 6\) and \(y=6\), we can also use the x - intercept. To find the x - intercept, set \(y = 0\) in the original equation \(5x-7(0)=7\), so \(5x=7\) and \(x=\frac{7}{5}=1.4\). So the line passes through \((1.4,0)\) and \((0, - 1)\). We can now plot these two points \((0,-1)\) and \((1.4,0)\) (or \((7,4)\) if we extend the graph) and draw the line.

Answer:

To graph \(5x - 7y = 7\) (or \(y=\frac{5}{7}x-1\)):

1. Plot the y - intercept at \((0,-1)\).
2. Use the slope \(\frac{5}{7}\) to find another point (e.g., from \((0,-1)\), move 7 units right and 5 units up to \((7,4)\) or find the x - intercept at \((\frac{7}{5},0)\approx(1.4,0)\)) and draw a straight line through these points.