which equations represent the line that is perpendicular to the line 5x − 2y = −6 and passes through the point (5, −4)? Select three options.y = –x – 22x + 5y = −102x − 5y = −10y + 4 = –(x – 5)y – 4 = (x + 5)
Accepted Solution
A:
Answer:y+4=-(2/5)(x-5) ----> equation of the line into point slope formy=-(2/5)x-2 ----> equation of the line into slope intercept form2x+5y=-10 ----> equation of the line in standard formStep-by-step explanation:step 1Find the slope of the given linewe have5x-2y=-6isolate the variable y2y=5x+6y=2.5x+3The slope m of the given line is m=2.5step 2Find the slope of the line perpendicular to the given lineWe know thatIf two lines are perpendicular, then their slopes are inverse reciprocal each othersom1=5/2the inverse reciprocal ism2=-2/5step 3Find the equation of the line into point slope form y-y1=m(x-x1)we havem=-2/5point (5,-4)substitutey+4=-(2/5)(x-5) ----> equation of the line into point slope formy=-(2/5)x+2-4y=-(2/5)x-2 ----> equation of the line into slope intercept formMultiply by 5 both sides5y=-2x-102x+5y=-10 ----> equation of the line in standard form