Question

1. a line has a y - intercept of 16 and an x - intercept of 4. another line is perpendicular to this line and has the same x - intercept of 4. what is the y - intercept of the second line? show how you found your answer.

Explanation:

Step1: Find the slope of the first line

The first line passes through points $(0,16)$ (y - intercept) and $(4,0)$ (x - intercept). The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. So, $m_1=\frac{0 - 16}{4-0}=\frac{-16}{4}=- 4$.

Step2: Find the slope of the second line

If two lines are perpendicular, the product of their slopes is - 1. Let the slope of the second line be $m_2$. Since $m_1\times m_2=-1$ and $m_1 = - 4$, then $-4\times m_2=-1$, so $m_2=\frac{1}{4}$.

Step3: Write the equation of the second line

The second line has an x - intercept of 4, so it passes through the point $(4,0)$. The slope - intercept form of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. Substitute $x = 4$, $y = 0$ and $m=\frac{1}{4}$ into $y=mx + b$. We get $0=\frac{1}{4}\times4 + b$.

Step4: Solve for the y - intercept of the second line

Simplify the equation $0=\frac{1}{4}\times4 + b$. First, $\frac{1}{4}\times4 = 1$, so the equation becomes $0 = 1 + b$. Then $b=-1$.

Answer:

-1