**Question 1:**A teacher told her class to write an equation of a line.Jack wrote down the equation \(4x + 6y = 8\) and Mary wrote down the equation \(3x - 7y = 10\).The students begin to discuss which line is steeper. Which line is steeper and why?---To determine which line is steeper, we need to compare the slopes of the two lines. To do this, we can rewrite each equation in slope-intercept form (\(y = mx + b\)), where \(m\) is the slope.1. **Equation 1: \(4x + 6y = 8\)** - Solve for \(y\): \[6y = -4x + 8\] \[y = -\frac{4}{6}x + \frac{8}{6}\] \[y = -\frac{2}{3}x + \frac{4}{3}\] - The slope (\(m\)) is \(-\frac{2}{3}\).2. **Equation 2: \(3x - 7y = 10\)** - Solve for \(y\): \[-7y = -3x + 10\] \[y = \frac{3}{7}x - \frac{10}{7}\] - The slope (\(m\)) is \(\frac{3}{7}\).**Comparison:**- The slope of the first line is \(-\frac{2}{3}\), and the slope of the second line is \(\frac{3}{7}\).- The absolute value of the first slope is \(\frac{2}{3} \approx 0.667\).- The absolute value of the second slope is \(\frac{3}{7} \approx 0.429\).Since \(\frac{2}{3} > \frac{3}{7}\), the line with the equation \(4x + 6y = 8\) is steeper. This is because the absolute value of its slope is greater.

Given: The line 4x+6y=8 and 3x-7y=10. To Find: the steeper line. Concept: The slope-intercept form of a line is y=mx+c. Where m is the slope of the line and c is the y-intercept. The steepness of a line: The steepness of a line is measured by the absolute value of the slope of the line. Therefore the steepness of a line y=mx+c is m.In order to find the slope of both of the lines we have to express them in the slope-intercept form. The line 4x+6y=8 can be written as 4x+6y=86y=-4x+8y=-46x+86y=-23x+43 So, the slope of the first line is m1=-23. The absolute value of the slope is m1=-23=23=0.67Similarly, find the slope of the line 3x-7y=10. The line 3x-7y=10 can be written as 3x-7y=10-7y=10-3xy=-3-7x+10-7y=37x-107 So, the slope of the second line is m2=37. The absolute value of the slope is m2=37=37=0.43. Now, the steepness of a line depends on the absolute value of the slope. As 0.67>0.43, The line 4x+6y=8 is steeper than the line 3x-7y=10. Since the absolute value of the slope of the line 4x+6y=8 is greater than the absolute value of the slope of the line 3x-7y=10 , the line 4x+6y=8 is steeper.