Question

The equation for line G is given by 5y=-2x-20. Suppose line G is parallel to line R, and line E is perpendicular to line G. Point (-10, 8) lies on both line R and line E. Choose the correct equation for R and E from the choices below.

Line E: y=5/x+33
Line R: y=-2/5x+4
Line E: y=5/2x+33
Line R: y=-2x+4
Line R: y=-5/2x+8

Answer 1

The correct equation for line R is y = -2x + 4, and the correct equation for line E is y = 5/2x + 33.

Step-by-step explanation:

Here's the reasoning:

Slope of line R:

Since line R is parallel to line G, they have the same slope.

The slope of line G can be found by rearranging its equation to slope-intercept form (y = mx + b): 5y = -2x - 20 --> y = -2/5x - 4

Therefore, the slope of line R is also -2/5.

Equation of line R:

We know line R passes through point (-10, 8) and has a slope of -2/5.

Using the point-slope form of a line, we get: y - 8 = -2/5(x + 10)

Simplifying, we get y = -2/5x + 4.

Slope of line E:

Line E is perpendicular to line G, so their slopes are negative reciprocals of each other.

The negative reciprocal of -2/5 is 5/2.

Equation of line E:

We know line E passes through point (-10, 8) and has a slope of 5/2.

Using the point-slope form again, we get: y - 8 = 5/2(x + 10)

Simplifying, we get y = 5/2x + 33.

Therefore, the correct equations for lines R and E are y = -2x + 4 and y = 5/2x + 33, respectively.

Answer 2

Line R, parallel to Line G, has the equation y = -2/5x + 4. Line E, perpendicular to Line G and going through the point (-10, 8), has the equation y = 5/2x + 33.

Step-by-step explanation:

The student is looking for the equations of two lines, Line R and Line E. Line R is parallel to Line G whose equation is 5y = -2x - 20, and Line E is perpendicular to Line G. Line G's slope is -2/5 (from the equation in the form 5y = -2x - 20, divided through by 5 to get y = -2/5x - 4). Given that Line R is parallel to Line G, it must have the same slope. The only choice provided with that slope is y = -2/5x + 4. Since Line E is perpendicular to Line G, its slope will be the negative reciprocal of Line G's slope, which is 5/2. The point (-10, 8) lies on Line E. To find the y-intercept, use the point-slope form of a line equation, y - y1 = m(x - x1), which becomes y - 8 = 5/2(x + 10). Multiplying through gives us y = 5/2x + 33. Therefore, the correct equations are Line E: y = 5/2x + 33 and Line R: y = -2/5x + 4.