The equation of line through given point is: [tex]y = \frac{7}{5}x+3[/tex]
Step-by-step explanation:
Given equation of line is:
[tex]y = \frac{7}{5}x-3[/tex]
Let m1 be the slope of given line and m2 be the slope of line parallel to given line.
As the given equation of line is in slope-intercept form, the o-efficient of x will be the slope of line
So,
[tex]m_1 = \frac{7}{5}[/tex]
As the new line is parallel to given line, slopes of both lines will be equal
[tex]m_1 = m_2 \\m_2 = \frac{7}{5}[/tex]
The slope-intercept form of equation is given by:
[tex]y= m_2x+b[/tex]
Putting the value of slope
[tex]y = \frac{7}{5}x+b[/tex]
To find the value of b putting (-5,-4) in the equation
[tex]-4 = \frac{7}{5}(-5)+b\\-4 = -7+b\\b = -4+7\\b = 3[/tex]
Putting the value of b
[tex]y = \frac{7}{5}x+3[/tex]
Hence,
The equation of line through given point is: [tex]y = \frac{7}{5}x+3[/tex]
Keywords: Slope-intercept form, equation of line
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