Question

given: $overleftrightarrow{ab}paralleloverleftrightarrow{cd}$. if the coordinates of point a are (8, 0) and the coordinates of point b are (3, 7), the y - intercept of $overleftrightarrow{ab}$ is. if the coordinates of point d are (5, 5), the equation of line $overleftrightarrow{cd}$ is y = x +.

Explanation:

Step1: Find the slope of line AB

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. For points $A(8,0)$ and $B(3,7)$, we have $x_1 = 8,y_1=0,x_2 = 3,y_2 = 7$. Then $m=\frac{7 - 0}{3 - 8}=\frac{7}{-5}=-\frac{7}{5}$.

Step2: Find the y - intercept of line AB

The equation of a line is $y=mx + b$. We know a point on line $AB$, say $A(8,0)$ and $m =-\frac{7}{5}$. Substitute into the equation: $0=-\frac{7}{5}\times8 + b$. Then $b=\frac{56}{5}$.

Step3: Find the equation of line CD

Since $\overleftrightarrow{AB}\parallel\overleftrightarrow{CD}$, they have the same slope. The equation of line $CD$ is in the form $y=mx + b$. Given a point on $CD$ say $(5,5)$ and $m =-\frac{7}{5}$. Substitute into $y=mx + b$: $5=-\frac{7}{5}\times5 + b$. Solving for $b$ gives $b=5 + 7=12$. So the equation of line $CD$ is $y=-\frac{7}{5}x+12$.

Answer:

The y - intercept of $\overleftrightarrow{AB}$ is $\frac{56}{5}$; the equation of line $\overleftrightarrow{CD}$ is $y =-\frac{7}{5}x + 12$