Question

(b)
What is the slope of the line joining the points (2,7) and (6,4) ?
Write the equation of this line.
If (x, y) is a point on this line, then prove that (x-4, y+3) is also a point on the same
line.​

Answer 1

Answer:

Let A (-2, 6), B (4, 8), P (8, 12), and Q be the specified points (x, 24). m1=864+2=26=13 is the slope of AB. PQ slope = m2 = 24 * 12 * 8 * 12 * 8 It is assumed that the lines connecting P (8, 12) and Q (x, 24) and A (-2, 6) and B (4, 8) are perpendicular. ∴ m1m2=−1⇒13×12x−8=−1⇒x−8=−4⇒x=4 Consequently, x has a value of 4.

Step-by-step explanation:

Step : 1 It is assumed that the lines connecting P (8, 12) and Q (x, 24) and A (-2, 6) and B (4, 8) are perpendicular. ∴ m1m2=−1⇒13×12x−8=−1⇒x−8=−4⇒x=4 Consequently, x has a value of 4. given that the line joining A (−2, 6) and B (4, 8) and the line joining P (8, 12) and Q (x, 24) are perpendicular. Hence, the value of x is 4.

Step : 2 A perpendicular is a straight line in mathematics that forms a right angle (90 degrees) with another line. In other words, two lines are perpendicular to one another if they connect at a right angle.

Step : 3  You may get the slope of the line by determining the rise and the run using two of the line's points. The rise and the run are terms used to describe changes in height between two places. Rise divided by Run gives you the slope. Run = rise + slope Rise + run = slope.

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