Question

1.) Write a​ slope-intercept equation for a line passing through the point (5,−3) that is parallel to the line 5x+7y=8.

Then write a second equation for a line passing through the point (5,−3) that is perpendicular to the line 5x+7y=8.

2.) Write a​ slope-intercept equation for a line passing through the point (4,−3) that is parallel to the line 4x+5y=7.

Then write a second equation for a line passing through the point (4,−3) that is perpendicular to the line 4x+5y=7.

3.) Write a​ slope-intercept equation for a line passing through the point (3,−3) that is parallel to the line x=−6.

Then write a second equation for a line passing through the point (3,−3) that is perpendicular to the line x=−6.

Answer 1

Solution:

(1) the given equation of line is .

Write this equation in the form of y=mx+c. So, the equation becomes,

------------------------------------- (1)

After comparing this equation with y=mx+c, we get slope (m₁) value as,

Now, we know the condition of parallel lines i.e. . So, .

Now, the equation of line passing through (x₁, y₁)=(5, -3) and slope, m₂=-5/7 is given by following equation,

This is the equation of parallel lines.

Now, Applying the condition of perpendicular lines i.e. . So, .

Now, the equation of line passing through (x₁, y₁)=(5, -3) and slope, m₂=7/5 is given by following equation,

This is the equation of perpendicular line.

(2). the given equation of line is .

Write this equation in the form of y=mx+c. So, the equation becomes,

So,

So, applying the condition of parallel lines, we have, .

The equation of line passing through point, (x₁, y₁)=(4, -3) and slope, m₂=-4/5 is,

This is the equation of parallel line.

Now, using the condition of perpendicular line, .

The equation of line passing through point, (x₁, y₁)=(4, -3) and slope, m₂=5/4 is,

this is the equation of perpendicular line.

(3).  the given equation of line is,

This line is parallel to y-axis. So, the slope of this line will be infinite OR undefined. . So, the slope of parallel line will also have the same slope, i.e. .

Now, using the equation of line passing through the point, (x₁, y₁)=(3, -3) and slope, . is,

This is the equation of parallel line to the line x=6 and passing through the point (3, -3).

Now, using the condition for the perpendicular line, .

So, the equation of line will be,

This is the equation of perpendicular line to the line x=6 and passing through the point (3, -3).