Answer:
Line [tex]b[/tex] is represented by the equation [tex]y = \frac{2}{5}\cdot x + 7[/tex].
Step-by-step explanation:
Let be line [tex]a[/tex] represented by [tex]2\cdot x - 5\cdot y = 15[/tex], whose explicitive form is:
[tex]5\cdot y = 2\cdot x - 15[/tex]
[tex]y = \frac{2}{5}\cdot x - 3[/tex]
As line [tex]b[/tex] is parallel to line [tex]a[/tex], its slope is equal to [tex]\frac{2}{5}[/tex]. 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 ([tex]k[/tex]):
[tex]y = \frac{2}{5}\cdot x +k[/tex]
If [tex]x = -10[/tex] and [tex]y = 3[/tex], then:
[tex]3 = \frac{2}{5}\cdot (-10)+k[/tex]
[tex]k = 3+\frac{2}{5} \cdot (10)[/tex]
[tex]k = 7[/tex]
Line [tex]b[/tex] is represented by the equation [tex]y = \frac{2}{5}\cdot x + 7[/tex].
