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To answer this question we must know coefficients in front of \(x\) in the equations of the lines.

Statement (1) by itself is insufficient. We do not know coefficients in front of \(x\) in the equations of the lines

Statement (2) by itself is insufficient. We do not know coefficients in front of \(x\) in the equations of the lines

Statements (1) and (2) combined are sufficient. Either \(K = 1\) and \(B = 0\) or vice versa. In either case, a line with slope 0 intersects a line with slope 1 at a 45-degree angle.

To answer this question we must know coefficients in front of \(x\) in the equations of the lines.

Statement (1) by itself is insufficient. We do not know coefficients in front of \(x\) in the equations of the lines

Statement (2) by itself is insufficient. We do not know coefficients in front of \(x\) in the equations of the lines

Statements (1) and (2) combined are sufficient. Either \(K = 1\) and \(B = 0\) or vice versa. In either case, a line with slope 0 intersects a line with slope 1 at a 45-degree angle.

Answer: C

Hi ! i have a doubt . so, i marked B as according to this formula - " tan(theta) = m1 - m2/1 + m1*m2" = ----taking B and K as the slope of either of the equations ----- as per Option B the denominator in my formula becomes 0 giving not defined solution ,which is the value of only Tan 90. Kindly correct me if im wrong.

I think this is a high-quality question and the explanation isn't clear enough, please elaborate. "a line with slope 0 intersects a line with slope 1 at a 45-degree angle." . Can you please elaborate on this with some relevant theory as to how to determine the angle with this information?

I think this is a high-quality question and the explanation isn't clear enough, please elaborate. "a line with slope 0 intersects a line with slope 1 at a 45-degree angle." . Can you please elaborate on this with some relevant theory as to how to determine the angle with this information?

A line with the slope of 0 is horizontal and a line with the slope of 1 is 45 degrees with x-axis, thus with the same 45 degrees with other horizontal lines.

y= mx+c , where m = tan(@) where @ is angle made with x axis so if we know two angles made by two lines on the xy plane, do we need to know the intercepts of line on y axis?

we say that two lines are perpendicular when m1*m2 =-1 where m1 and m2 are slopes of two different lines, example tan30 = 1/root 3 , tan120= -root3 = -tan60

so angle between two lines = 120-30= 90

if BK = m1m2= 0 , means either B IS 0 OR K =0, when one of the slope is 0, it means te line is parallel to x axis, example slope m1 = y2-y1/x2-x1 , take two points (5, 3) , (7,3) so m= 3-3/7-5 = 0 . this line has two points whose cordinates have same y distance from the x axis, means parallel to x axis

same way if line is parallel to y axis slope is infinity

also when slope is 1 , it means y2-y1= x2-x1= so tan45=1 so angle is 45 so combining 1 and 2 we get two lines one with slope 0 and one with slope 45

At what angle do lines \(y = Kx + B\) and \(y = Bx + K\) intersect ?

(1) \(B + K = 1\)

(2) \(BK = 0\)

we know tanA = (m1-m2)/(1+m1m2) where "A" is the angle between the lines and "M1 and M2" are slopes i) knowing B+ K we cannot find M1-M2 or M1M2 :insufficient ii)knowing M1M2 we cannot find M1-M2 : insufficient

combining i) and ii) we get K-B as 1 or -1 ,as case1: B=0 and K=1 case2: B=-1 and K=0 but inverse tan of 1 and -1 will give you a 45 degree between: them so combining is sufficient

B*K = 0 => K* ( 1 - K) = 0 Hence K = 0 or K = 1 for K = 0 , B = 1 and for K = 1 , B = 0

Let K = 1 and B = 0 line 1: y = Kx + B Here slope , K = 1 . hence the line is 45° to the y-axis line 2: y = Bx + K Here the slope , B = 0 . hence the line is 90° to the y-axis

Therefore the lines intersect at 45°angle. Hence sufficient