Question

Could someone help me understand how to solve this please, thank you!

Answer 1

The equation of required line is: $y=\frac{-1}{4}x+\frac{5}{4}$

Step-by-step explanation:

We are given point (1,1) and a line having equation y=4x+6

We need to find a line perpendicular to the given line.

The standard form of slope-intercept is: y=mx+b

where m is slope and b is y-intercept.

So, comparing the given equation with standard line we get,

m= 4

Since the new line is perpendicular to the given line, so its slope will be -1/slope

So, slope of new line is m= -1/4

Now, finding y-intercept

Using the given point and slope we get:

$y=mx+b\\1=\frac{-1}{4}(1)+b\\1=\frac{-1}{4}+b\\b=1+\frac{1}{4}\\b=\frac{4+1}{4}\\b=\frac{5}{4}$

So, y-intercept is $b=\frac{5}{4}$

The equation of new line having slope -1/4 and y-intercept = 5/4 is:

$y=mx+b\\y=\frac{-1}{4}x+\frac{5}{4}$

So, the equation of required line is: $y=\frac{-1}{4}x+\frac{5}{4}$

Keywords: Slope-intercept form is:

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