Question

determine whether the lines are parallel, intersect, or coincide
y=1/3x+4
x-3y=-12

Answer 1

The slopes of two lines are equal which means that the lines are parallel.

Further explanation:

The slopes of lines are used to find the relationship between two line.

• If two lines are parallel, then their slopes will be equal.
• If two lines are perpendicular, the product of slopes of both lines will be -1

The standard form of equation of line is:

$y=mx+b$

The coefficient of x is the slope here.

y=1/3x+4

Let m1 be the slope of first line:

$m_1=\frac{1}{3}$

$x-3y=-12\\-3y=-x-12\\-3y=-1(x+12)\\3y=x+12\\\frac{3y}{3}=\frac{x+12}{3}\\y=\frac{x+12}{3}\\y=\frac{x}{3}+\frac{12}{3}\\y=\frac{1}{3}x+4$

Let m2 be the slope of second line

$m_2=\frac{1}{3}$

We can see that:

$m_1=m_2$

The slopes of two lines are equal which means that the lines are parallel.

Keywords: Parallel Lines, Perpendicular Lines

Learn more about lines at:

• brainly.com/question/3552621
• brainly.com/question/3617539

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