Divide both sides of the given equation by –2 to put the equation in slope-intercept form (y= mx + b); –2y = –8x + 10 is equivalent to y = 4x – 5. The slope of this line is the coefficient of x, 4. The slopes of perpendicular lines are negative reciprocals of each other. The negative reciprocal of 4 is –¹⁄₄. Only choice b is a line with a slope of –¹⁄₄.

Divide both sides of the equation by 4 to put the given equation in slope-intercept form (y = mx + b); 4y = 6x – 6 is equivalent to y = ³⁄₂ (x) – ³⁄₂. The slope of this line is the coefficient of x, ³⁄₂. Parallel lines have identical slopes. Only choice d is a line with a slope of ³⁄₂.

The slopes of perpendicular lines are negative reciprocals of each other. When an equation is written in slope-intercept form (y = mx + b), the slope of the line is m. The slope of the line y = –¹⁄₆(x) + 8 is –¹⁄₆. The negative reciprocal of –¹⁄₆ is 6. Only choice e is a line with a slope of 6.

Parallel lines have identical slopes. When an equation is written in slope-intercept form (y = mx + b), the slope of the line is m. The slope of the line y = –2x + 4 is –2. Only choice a is a line with a slope of –2.

Divide both sides of the equation by 5 to put the equation in slope-intercept form (y = mx + b); 5y = –3x + 6 is equivalent to y = –³⁄₅ x + ⁶⁄₅. The slope of this line is the coefficient of x, –³⁄₅.

The coordinates of point C are (–3,6) and the coordinates of point D are (5,–6). To find the distance between two points, use the distance formula:

D = \(\sqrt{((x_{2}-x_{1})^{2}+(y_{2}+y_{1})^{2})}\)

D = \(\sqrt{((5-(-3))^{2}+((-6)-6)^{2})}\)

D = \(\sqrt{((5-(-3))^{2}+((-6)-6)^{2})}\)

D = \(\sqrt{((5-(-3))^{2}+((-6)-6)^{2})}\)

D = \(\sqrt{208}=\sqrt{16}\sqrt{13}=4\sqrt{13}\)units

The coordinates of point A are (–5,–4) and the coordinates of point B are (9,2). To find the distance between two points, use the distance formula:

D = \(\sqrt{((x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2})}\)

D = \(\sqrt{((7-3)^{2}+((-6)-8)^{2})}\)

D = \(\sqrt{((7-3)^{2}+((-6)-8)^{2})}\)

D = \(\sqrt{16+196}\)

D = \(\sqrt{16+196}\) = √4\(\sqrt{58}\) = 2\(\sqrt{58}\)units

To find the distance between two points, use the distance formula:

D = \(\sqrt{((x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2})}\)

D = \(\sqrt{((7-3)^{2})+((-6)-8)^{2}}\)

D = \(\sqrt{(4^{2}+(-14)^{2})}\)

D = \(\sqrt{(16+196)}\)

D = \(\sqrt{232}\) = √4\(\sqrt{53}\) = 2\(\sqrt{53}\) units

To find the distance between two points, use the distance formula:

D = \(\sqrt{((x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2})}\)

D = \(\sqrt{((x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2})}\)

D = \(\sqrt{((x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2})}\)

D = \(\sqrt{(16+64)}\)

D = \(\sqrt{(16+64)}\) = \(\sqrt{16}\)√5=4√5 units

To find the distance between two points, use the distance formula:

\(D=\sqrt{((x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2})}\)

\(D=\sqrt{((2-(-6))^{2}+(17-2)^{2})}\)

\(D=\sqrt{(8^{2}+(15)^{2})}\)

\(D=\sqrt{(8^{2}+(15)^{2})}\)

D=\(\sqrt{289}\)= 17 units