Consider the line that passes through the point P(4, - 2) and is parallel to the line - 3x - 4y = 2 Write the point-slope equation of the line. Use exact values.

9514 1404 393

  y +2 = -3/4(x -4)

Step-by-step explanation:

A line parallel to ...

  ax +by = c

through point (h, k) can have the equation ...

  a(x -h) +b(y -k) = 0

It is pretty simple to put this into point-slope form:

  b(y -k) = -a(x -h) . . . . . subtract the x-term

  y -k = (-a/b)(x -h) . . . . divide by b

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We have ...

  a = -3, b = -4, (h, k) = (4, -2)

so the point-slope form equation is ...

  y -(-2) = (-(-3)/(-4))(x -4)

  y +2 = -3/4(x -4)

The correct answer is .44

Answer: question no. 1 -a. yes, the sides are in the ratio 2 : 5.question no. 2 -b. 59°question no. 3 -c. angles x and y are remote interior angles.question no. 4 -d. 90°, 45° and 45°question no. 5 -b. mn and qrstep-by-step explanation: question no. 1 -rs : xu = 3 : 7.5 = 2 : 5rt : x? = 6.4 : 16 = 2 : 5st : u? = 6 : 15 = 2 : 5as the ratios of all sides are equivalent, the triangles must be congruent and the sides must be proportional.therefore, the answer is: a. yes, the sides are in the ratio 2 : 5.question no. 2 -in the second diagram, angle b is the only letter not shown. therefore, the number must be equivalent to angle b.if we substitute the value of angle b as being 22° in the first diagram, we can now use the angle sum of a triangle to obtain the value of angle a.angle sum of a triangle = 180°therefore: let angle a = aa + 99 + 22 = 180a = 180 - 99 - 22a = 59°therefore, the answer is: b. 59°question no. 3 -angles x and y don't share the vertex of the triangle with the exterior angle w. remote interior angles don't share a vertex of a triangle with an exterior angle. this means that angles x and y are remote interior angles.therefore, the answer is: c. angles x and y are remote interior angles.question no. 4 -the sum of all interior angles of a triangle must be equivalent to 180°.90°, 45° and 45° are the only set of angle measures that are equivalent to 180°.therefore, the answer is: d. 90°, 45° and 45°question no. 5 -the only pair of sides stated in the options which are corresponding are mn and qr.therefore, the answer is: b. mn and qr.