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Mandarinka [93]
3 years ago
12

4. Write an equation for the line that is parallel to the given line and that passes

Mathematics
1 answer:
pentagon [3]3 years ago
4 0

Answer:

y=\frac{5}{2}x-14

Step-by-step explanation:

Hi there!

<u>What we need to know:</u>

  • Linear equations are typically organized in slope-intercept form: y=mx+b where m is the slope and b is the y-intercept (the value of y when x is 0)
  • Parallel lines always have the same slope

<u>1) Determine the slope (m)</u>

y=\frac{5}{2}x-10

In the given equation, \frac{5}{2} is in the place of m, making it the slope. Because parallel lines have the same slope, the line we're currently solving for therefore has a slope of \frac{5}{2}. Plug this into y=mx+b:

y=\frac{5}{2}x+b

<u>2) Determine the y-intercept (b)</u>

y=\frac{5}{2}x+b

Plug in the given point (-6,-29) and solve for b

-29=\frac{5}{2}(-6)+b

Simplify -6 and 2

-29=\frac{5}{1}(-3)+b\\-29=(5)}(-3)+b\\-29=-15+b

Add 15 to both sides to isolate b

-29+15=-15+b+15\\-14=b

Therefore, the y-intercept is -14. Plug this back into y=\frac{5}{2}x+b:

y=\frac{5}{2}x-14

I hope this helps!

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