Answer:
[tex]y=\frac{5}{4}x-8[/tex]
Step-by-step explanation:
Hi there!
What we need to know:
- Linear equations are typically organized in slope-intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept (the value of y when the line crosses the y-axis)
- Parallel lines always have the same slopes and different y-intercepts
1) Determine the slope (m)
[tex]5x - 4y = 36[/tex]
Rearrange the given equation into y-intercept form (this will help us determine m)
Subtract 5x from both sides
[tex]5x - 4y-5x = -5x+36\\-4y=-5x+36[/tex]
Divide both sides by -4
[tex]y=\frac{5}{4} x-9[/tex]
Now, we can see that [tex]\frac{5}{4}[/tex] is in the place of m, making it the slope. Because parallel lines have the same slopes, the slope of the line we're solving for is therefore [tex]\frac{5}{4}[/tex]. Plug this into [tex]y=mx+b[/tex]:
[tex]y=\frac{5}{4}x+b[/tex]
2) Determine the y-intercept (b)
[tex]y=\frac{5}{4}x+b[/tex]
Plug in the given point (8,2) and solve for b
[tex]2=10+b[/tex]
Subtract 10 from both sides
[tex]2-10=10+b-10\\-8=b[/tex]
Therefore, the y-intercept is -8. Plug this back into [tex]y=\frac{5}{4}x+b[/tex]:
[tex]y=\frac{5}{4}x-8[/tex]
I hope this helps!
