To find two equations of lines that are parallel to the given line \( y = \frac{3}{4}x - 6 \), we need to keep the same slope as the original line, since parallel lines have equal slopes.
-
Identify the slope of the given line: The slope-intercept form of a line is \( y = mx + b \), where \( m \) is the slope. From the equation \( y = \frac{3}{4}x - 6 \), we see that the slope \( m \) is \( \frac{3}{4} \).
-
Write two parallel equations: Using the same slope \( \frac{3}{4} \), we can create two different linear equations in slope-intercept form by choosing different y-intercepts (the \( b \) value) while keeping the same slope.
-
Equation 1: Let's choose \( b = 2 \): \[ y = \frac{3}{4}x + 2 \]
-
Equation 2: Let's choose \( b = -1 \): \[ y = \frac{3}{4}x - 1 \]
-
-
Verification of parallelism: Both equations \( y = \frac{3}{4}x + 2 \) and \( y = \frac{3}{4}x - 1 \) have the same slope of \( \frac{3}{4} \) as the original line. Therefore, they will never intersect, confirming that they are parallel to the given line.
Summary
The two equations of lines parallel to \( y = \frac{3}{4}x - 6 \) are:
- \( y = \frac{3}{4}x + 2 \)
- \( y = \frac{3}{4}x - 1 \)
These lines are parallel because they share the same slope, \( \frac{3}{4} \).