The slope of line perpendicular to given line is is 3/2 and y-intercept is: -1/2
Step-by-step explanation:
Given equation of line:
[tex]y = -\frac{2}{3}x+5[/tex]
The given equation of line is in slope-intercept form so the co-efficient of x will be the slope of the line
Let m_1 be the slope of given line
[tex]m_1 = -\frac{2}{3}[/tex]
As we know that the product of slopes of perpendicular lines is -1
Let m_2 be the slope of required line
So,
[tex]m_1.m_2= -1\\-\frac{2}{3} . m_2 = -1\\m_2 = -1 * -\frac{3}{2}\\m_2 =\frac{3}{2}[/tex]
The lope-intercept form is:
[tex]y =m_2x+b[/tex]
Putting the value of m2
[tex]y = \frac{3}{2}x+b[/tex]
To find the value of y-intercept, putting (5,7) in the equation
[tex]7 = \frac{3}{2}(5) + b\\7 = \frac{15}{2} + b\\7 - \frac{15}{2} = b\\b =\frac{14-15}{2}\\b = -\frac{1}{2}[/tex]
Putting the values of slope and y-intercept
[tex]y = \frac{3}{2}x - \frac{1}{2}[/tex]
Hence,
the slope is 3/2 and y-intercept is: -1/2
Keywords: Slope, y-intercept
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