Question

1. graph: $y = \frac{3}{4}x$
2. solve: $\frac{e}{5} = \frac{5}{6}$

Explanation:

Problem 12: Graph \( y = \frac{3}{4}x \)

Step 1: Identify the type of equation

The equation \( y = \frac{3}{4}x \) is a linear equation in the form \( y = mx \), where \( m \) is the slope. Here, the slope \( m=\frac{3}{4} \) and the y - intercept is \( 0 \) (since there is no constant term), so the line passes through the origin \((0,0)\).

Step 2: Find another point using the slope

The slope \( \frac{3}{4} \) means "rise over run", or \( \frac{\text{change in }y}{\text{change in }x} \). Starting from the origin \((0,0)\), if we move \( 4 \) units to the right (increase \( x \) by \( 4 \), so \( \Delta x = 4 \)), we then move up \( 3 \) units (increase \( y \) by \( 3 \), so \( \Delta y=3 \)). This gives us the point \((0 + 4,0+ 3)=(4,3)\).

Step 3: Plot the points and draw the line

Plot the points \((0,0)\) and \((4,3)\) on the coordinate grid. Then, draw a straight line passing through these two points. We can also find other points for verification. For example, if \( x=- 4 \), then \( y=\frac{3}{4}\times(-4)=-3 \), so the point \((-4,-3)\) is also on the line.

Problem 14: Solve \( \frac{e}{5}=\frac{5}{6} \)

Step 1: Cross - multiply

To solve for \( e \) in the proportion \( \frac{e}{5}=\frac{5}{6} \), we use the cross - multiplication property of proportions. If \( \frac{a}{b}=\frac{c}{d} \), then \( a\times d=b\times c \). Here, \( a = e \), \( b = 5 \), \( c = 5 \), and \( d = 6 \). So we have \( e\times6=5\times5 \).

Step 2: Simplify and solve for \( e \)

Simplify the right - hand side: \( 5\times5 = 25 \), so the equation becomes \( 6e=25 \). Then, divide both sides of the equation by \( 6 \) to isolate \( e \). We get \( e=\frac{25}{6}\approx4.17 \) (if we want a decimal approximation).

Answer:

s:

• For problem 12: The graph is a straight line passing through \((0,0)\), \((4,3)\), \((-4,-3)\) etc. (plotted on the given grid).
• For problem 14: \( e=\frac{25}{6} \) (or \( e\approx4.17 \))