Question

What is an equation of the line that passes through the point (-5,6) and is parallel to the line 3x+5y=45

Answer 1

Answer:

$y = \frac{ - 3x}{5} + 3$

Step-by-step explanation:

Change 3x + 5y = 45 to slope intercept form.

$5y = - 3x + 45 \\ \frac{5y}{5} = \frac{ - 3x}{5} + \frac{45}{5} \\ y = \frac{ - 3x}{5} + 9$

A parallel line has the same slope, therefore, the new equation's slope would be

$\frac{ - 3}{5}$

Using point slope form

$y - y1 = m(x - x1) \\ y - 6 = \frac{ - 3}{5} (x + 5) \\ y - 6 = \frac{ - 3x}{5} - 3 \\ y = \frac{ - 3x}{5} + 3$