Lines

1. Find the equation of each vertical line that passes through the point

(a) \(\displaystyle{(-2,5)}\)       (b) \(\displaystyle{(3,-7)}\).              Ans: (a) \( x = -2 \),  (b)  \( x = 3\).

2. Find the equation of each horizontal line that passes through the point

(a) \(\displaystyle{(2,-5)}\)      (b) \(\displaystyle{(-3,-2)}\).              Ans: (a) \( y = -5 \),  (b)  \( y = -2\).

3. What is the slope of a vertical line? What is the slope of a horizontal line?   (vert line = undefined, horiz line = 0)

4. Find the equation of the line passing through the point \(\displaystyle{(2,-5)}\) with slope 2. Write your answer in slope-intercept form.    solution

5. Find the equation of the line passing through the points \(\displaystyle{(-1,-2)}\) and \(\displaystyle{(-5,6)}\). Write your answer in slope-intercept form.   solution

6. Write an equation of the line that  has \(\displaystyle{x}\)-intercept \(-6\) and  \(\displaystyle{y}\)-intercept \(9\).    solution

7. Find the slope and the \(\displaystyle{y}\)-intercept of the line with the equation \(\displaystyle{5x - 3y + 11 = 20}\).    solution

8. Determine whether each pair of lines are parallel, perpendicular, or neither.   solution

(a) \( 2x+3y=7 \) and \(y=2\)           (b)   \( x-4y=7 \) and \(y=-4x-2\)

9. Find the value of \(k\) so that the lines \(x+2y-7=0\) and \( kx-4y+2=0\) are perpendicular.   solution

10. Find the equation of the line parallel to \(\displaystyle{5x - 2y + 8 = 0}\) and passing through the point \(\displaystyle{(-1,2)}\).   solution

11. Find the equation of the line perpendicular to \(\displaystyle{2x + 6y = 8}\) and passing through the point \(\displaystyle{(1,-2)}\).   solution