Question

Suppose the equation for line a is given by 2x-5y=15. If line a and b are parallel and the point (-10, 3) lies on line b, then write the equation in slope intercept form for line b

Answer 1

Answer:

Line $b$ is represented by the equation $y = \frac{2}{5}\cdot x + 7$.

Step-by-step explanation:

Let be line $a$ represented by $2\cdot x - 5\cdot y = 15$, whose explicitive form is:

$5\cdot y = 2\cdot x - 15$

$y = \frac{2}{5}\cdot x - 3$

As line $b$ is parallel to line $a$, its slope is equal to $\frac{2}{5}$. Two lines that are parallel to each other have the same slope but different y-intercept. In addition, we know that point (-10, 3) lies on that line and we must find the y-intercept ($k$):

$y = \frac{2}{5}\cdot x +k$

If $x = -10$ and $y = 3$, then:

$3 = \frac{2}{5}\cdot (-10)+k$

$k = 3+\frac{2}{5} \cdot (10)$

$k = 7$

Line $b$ is represented by the equation $y = \frac{2}{5}\cdot x + 7$.