Question

What do the following two equations represent

Answer 1

c) perpendicular lines

Explanation:

Given equation:

• 4x - 2y = -5 Green line
• 
  `y = -(1)/(2) x - (1)/(10)` Red line

We can rewrite the first equation in slope-intercept form:

`\sf 4x - 2y = -5`

`\sf -2y = -4x - 5`

`\sf y = 2x + (5)/(2)`

This gives us the slope and y-intercept of the first line, which are 2 and 5/2, respectively.

The second equation is already in slope-intercept form, with a slope of -1/2 and a y-intercept of -1/10.

Since the slopes are not equal, the lines are not the same. The slope of the first equation is 2, and the negative reciprocal of 2 is -1/2, which is the slope of the second equation.

Therefore, the two lines are perpendicular.

so, the answer is c) perpendicular lines