Question

30 POINTS NEED HELP ASAP!! What is an equation of the line that passes through the point (-5, 3) and is parallel to the line 4x - 5y = 25?

Answer 1

Answer: the equation of the line that passes through the point (-5, 3) and is parallel to the line 4x - 5y = 25 is y = (4/5)x + 7

Answer 2

The equation of the line passing through the point (-5, 3) and parallel to the line 4x - 5y = 25 is y = -4/5x - 4, obtained by using the slope-intercept form to find the slope and then applying the point-slope form.

Step-by-step explanation:

The question asks for an equation of a line that passes through a given point (-5, 3) and is parallel to another given line, 4x - 5y = 25. Since parallel lines have the same slope, the first step is to find the slope of the given line. We rearrange the equation into slope-intercept form (y = mx + b) to find the slope.

1. Convert the given line to slope-intercept form:
   
2. The slope (m) of the line is -4/5.

Now, using the point-slope form (y - y1 = m(x - x1)), we can find the equation of the new line:

1. Insert the slope and the given point into the point-slope form:
2. y - 3 = -4/5(x - (-5))
3. 
   
4. 
   
5. = -4/5(x + 5)
6. Rewriting the equation in slope-intercept form (if needed):
7. 
   
8. y = -4/5x - 4
9. 
   
10. 
    
11. = -4/5x - 20/5
12. 
    
13. 
    
14. = -4/5x - 4

The equation of the line passing through (-5, 3) and parallel to the line 4x - 5y = 25 is y = -4/5x - 4.