Question

What is an equation of the line that passes through the point(5,-3) and is parallel to the line 4x-5y=45

Answer 1

The equation of line that passes through the point(5,-3) and is parallel to the line 4x-5y=45 is: $y = \frac{4}{5}x-7$

Step-by-step explanation:

Given equation is:

$4x-5y = 45$

First of all we have to convert the equation in slope-intercept form

So,

$4x - 45 = 5y\\5y = 4x-45\\\frac{5y}{5} = \frac{4x-45}{5}\\y = \frac{4x}{5} -\frac{45}{5}\\y = \frac{4}{5}x - 9$

Let m1 be the slope of given line and m2 be the slope of required line

The coefficient of x is the slope of the line, so

m1 = 4/5

As the required line is parallel to given line, both will have equal slopes

m2 = 4/5

Slope-intercept form is:

$y = m_2x+b$

Putting the value of m2

$y = \frac{4}{5}x +b$

Putting the point (5,-3) in the equation

$-3 = \frac{4}{5} (5) +b\\-3 = 4+b\\b = -3-4\\b = -7$

Putting the value of b

$y = \frac{4}{5}x-7$

Hence,

The equation of line that passes through the point(5,-3) and is parallel to the line 4x-5y=45 is: $y = \frac{4}{5}x-7$

Keywords: Slope, equation of line

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