Write an equation for a line perpendicular to y = -5x – 4 and passing through the point (15,5)
1 answer:
The equation for the line in point-slope form that passes through (15, 5) and is perpendicular to is
<em><u>Recall:</u></em>
The equation of the line can be written in point-slope form (y - b = m(x - a)) and also in slope-intercept form (y = mx + b).
<em><u>Given</u></em>:
- the point the line passes through: (15, 5)
- the line it is perpendicular to: y = -5x - 4
<u><em>Find the </em></u><u><em>slope (m):</em></u>
The slope value will be the negative reciprocal of the slope value of y = -5x - 4.
- The slope of y = -5x - 4 is -5.
- Therefore, the slope of the line perpendicular to y = -5x - 4 will be the negative reciprocal of -5 which is: 1/2.
<em>Write the </em><em>equation </em><em>in </em><em>point-slope</em><em> form by substituting m = 1/2 and (a, b) = (15, 5) into </em><em>y - b = m(x - a)</em>
<em />
- Thus:
Therefore, the equation for the line that passes through (15, 5) and is perpendicular to is
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A Quadrilateral A B C D in which Sides AB and DC are congruent and parallel.
The student has written the following explanation
Side AB is parallel to side DC so the alternate interior angles, angle ABD and angle BDC, are congruent. Side AB is equal to side DC and DB is the side common to triangles ABD and BCD. Therefore, the triangles ABD and CDB are congruent by SAS.
The student has also written
angles DBC and ADB are congruent and sides AD and BC are congruent. Angle DBC and angle ADB form a pair of alternate interior angles. Therefore, AD is congruent and parallel to BC. Quadrilateral ABCD is a parallelogram because its opposite sides are equal and parallel.
Postulate SAS completely describes the student's proof.
Because if in a quadrilateral one pair of opposite sides are equal and parallel then it is a parallelogram.
