Equation of a Straight Line: Point-Slope Form of a Line

Examples with solutions for Equation of a Straight Line: Point-Slope Form of a Line

Exercise #1

Straight line passes through the point (2,13) (-2,-13) and parallel to the line 4+y=5x6 -4+y=5x-6

Video Solution

Step-by-Step Solution

First, let's arrange the line equations:

4+y=5x6 -4+y=5x-6

y=5x+46 y=5x+4-6

y=5x2 y=5x-2

From here we can determine the slope:

m=5 m=5 We'll use the formula:

y=mx+b y=mx+b

We'll use the point (2,13) (-2,-13)

13=5×2+b -13=5\times-2+b

13=10+b -13=-10+b

3=b -3=b

Let's substitute the existing data back into the formula:

y=5x+(3) y=5x+(-3)

y=5x3 y=5x-3

Answer

y=5x3 y=5x-3

Exercise #2

Straight line passes through the point (6,14) (6,14) and parallel to the line x+3y=4x+9 x+3y=4x+9

Video Solution

Answer

y=x+8 y=x+8

Exercise #3

Straight line passes through the point (5,12) (-5,12) and parallel to the line 5y5x=15 5y-5x=15

Video Solution

Answer

yx=17 y-x=17

Exercise #4

Straight line passes through the point (0,1) (0,1) and parallel to the line 2(y+1)=16x 2(y+1)=16x

Video Solution

Answer

y8x=1 y-8x=1

Exercise #5

A line passes through the point (2,9) (2,9) and is perpendicular to the line y=15x+3 y=-\frac{1}{5}x+3 .

Choose the corresponding function.

Video Solution

Answer

y=5x1 y=5x-1

Exercise #6

Which function represents a straight line that passes through the point (3,15) (-3,-15) and is perpendicular to the line
3y=4xy 3y=4x-y ?

Video Solution

Answer

y+x=18 y+x=-18

Exercise #7

Which function represents a straight line that passes through the point (0,0) (0,0) and is perpendicular to the line y2x=2y y-2x=2y ?

Video Solution

Answer

y=12x y=\frac{1}{2}x

Exercise #8

Which function describes a straight line that passes through the point (7,2) (7,2) and is perpendicular to the line 3y=x+12 3y=x+12 ?

Video Solution

Answer

y=3x+23 y=-3x+23