Chapter 2 Section [2.4]

When give the slope (m) and a point (x₁, y₁), you can use the point-slope formula to write an equation for a line.

The point-slope formula is: y-y₁=m(x-x₁)

Example # 1

Write an equation of the line that passes through (2,3) and has a slope of -1/2.

m= -1/2, (x₁, y₁)= (2,3)

Plug in the given information into the point-slope equation.

y-3= -1/2(x-2)

Simplify the equation into slope-intercept form.

Distribute the -1/2 to the x and -2.

y-3= -1/2x+1

Add 3 to both sides.

y-3+3= -1/2x+1+3

Answer: y= -1/2+4

Example # 2

Write an equation of the line that passes through (1, -1) and is perpendicular to the line y= -1/2x+6.

Take the positive reciprocal of -1/2, to find the slope.

Plug the given information into the point-slope formula.

y-(-1)= 2(x-1)

Then distribute the 2 to the x and -1.

y+1= 2x-2

Subtract 1 from both sides.

Y+1-1= 2x-2-1

Answer: y=2x-1

Example # 3

Write an equation of the line that passes through (3, 2) and is parallel to the line y= -3x+4.

The line is parallel, therefore the new line will have the same slope, -3.

Plug the given information into the point-slope formula.

y-2= -3(x-3)

Then distribute the -3 to the x and the -3.

y-2= -3x+9

Add 2 to both sides.

y-2+2= -3x+9+2

Answer: y= -3x+11

Practice Problems

1.) Write an equation of a line using the point-slope formula, with this given information: m=2, (0, 4)

2.) Write an equation of the line that passes through (2, -7) and is parallel to the line x=5.

3.) Write an equation of the line that passes through (1, -1) and is perpendicular to the line y= -1/2x+6.