Writing Equations of Lines

Find an equation of the line that has a slope 1/2 and passes through the point (-6,5). Write in standard form.

*Use the point-slope form* Y-y1=m(x-x1) *Substitute 5 for y1, 1/2 for m, and -6 for x1. y-(5)= (1/2) (x-(-6)) *Write the subtraction of -6 as addition* y-(5)=1/2(x+6) *Distribute 1/2 over the expression in parentheses* y-5=1/2x+3 *Add 5 to both sides. This is in slope-intercept form* y=1/2x+8 *Subtract 1/2x from each side* -1/2x+y=8 *Multiply each side by 2 to clear the fraction. This is in standard form* -x+2y=16

Find an equation of the line that passes through the points (3,2) and (5,8)

*Use the slope formula to find the slope of the line* m=y2-y1/x2-x1= (8)-(2)/(5)-(3)= 6/2= 3 *Choose either point* Let x1 = 3 and y1 = 2. Use (3,2) because these numbers are easier to work with than (5,8) *Substitute values into point-slope form* y-y1=m(x-x1) y-(2)=(3)(x-(3)) Substitute 2 for y1, 3 for m, and 3 for x1 *Simplify* y-2=3(x-3) y-2=3x-9 y=3x-7 Distribute. Add 2 to each side. The equation is in slope-intercept form.

What is the slope of y=2?

All horizontal lines have slopes of 0

What is the slope of x=-5?

All vertical lines have slopes that are undefined

Two points on the line

Find the slope. Then substitute m and the coordinates y-y1=m(x-x1)

Slope and y-intercept

Substitute the values for m and b into y=mx+b

Slope and point on the line

Substitute the values for x1, y1, and m into y-y1=m(x-x1)

Parallel lines

have equal slopes

Perpendicular lines

haves slopes that are opposite reciprocals of each other

Find the slope of the line that passes through the points (0,10) and (3,-5)

slope= 10−(−5)/0−3=15/−3=−5 slope=−5−10/3−0=−15/3=−5

Find the slope of the line that passes through the points (-3,4) and (5,6)

slope= 6−4/5−(−3)=2/8=1/4 slope=4−6/(−3)−5=−2/−8=1/4