Question

determine whether the graphs of the pair of equations are parallel, perpendicular, or neither.
y = 4x + 3
4x + y = 3

Explanation:

Step1: Rewrite the second equation in slope - intercept form

The general form of the slope - intercept form of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept.
We have the equation $4x + y=3$. Solve for $y$:
Subtract $4x$ from both sides of the equation: $y=-4x + 3$.

Step2: Identify the slopes of the two lines

For the first equation $y = 4x+3$, the slope $m_1$ is $4$.
For the second equation $y=-4x + 3$, the slope $m_2$ is $- 4$.

Step3: Check for parallel or perpendicular lines

• Parallel lines have equal slopes. Since $m_1 = 4$ and $m_2=-4$, $m_1

eq m_2$, so the lines are not parallel.

• Perpendicular lines have slopes that are negative reciprocals of each other. The negative reciprocal of $4$ is $-\frac{1}{4}$, and the negative reciprocal of $-4$ is $\frac{1}{4}$. Since $m_1\times m_2=(4)\times(-4)=-16

eq - 1$, the lines are not perpendicular.

Answer:

The graphs of the pair of equations are neither parallel nor perpendicular.