Question

Write an equation of the line that passes through 7,10 and is perpendicular to the line y=1/2-9

Answer 1

An equation of the line that passes through (7,10) and is perpendicular to the line y=1/2x-9 is $y=-2x+24$

Step-by-step explanation:

We need to write an equation of the line that passes through 7,10 and is perpendicular to the line y=1/2x-9

Note: Considering the line y=1/2x-9

For finding an equation of line we need

• Slope (m)
• y-intercept (b)

The general equation of slope intercept form used is:

$y=mx+b$

The equation of line given is: y=1/2x-9

The new line is perpendicular to the given line So, the slope of new line would be m = -1/m

So, Slope of given line m = 1/2

Slope of required line = -1/m = -2

So, m= -2

Now, for finding y-intercept (b) we need slope m = -2 and the point given (7,10)

Putting values of m, x=7 and y = 10 in the equation of slope intercept form

$y=mx+b\\10=-2(7)+b\\10=-14+b\\b=10+14\\b=24$

So, Equation of required line having slope m = -2 and y-intercept b = 24

$y=mx+b\\y=-2x+24$

An equation of the line that passes through (7,10) and is perpendicular to the line y=1/2x-9 is $y=-2x+24$

Keywords: Equation of line using Slope  

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