Question

1. Write the equation of the line with a slope of -5 and a y-intercept of (0,3). 2. Write the equation of the line with a slope of -1/3 and passing through the point (6, -4). 3. Write the equation of the line passing through the points (0, -4) and (-2, 2). 4. Write the equation of the line passing through the points (-6,1) and (-4,2). 5. Write the equation of the line with an undefined slope, passing through the point (2, 5). Hint: refer back to lesson 4.04 for help with this one.

Answer 1

Explanation:

1) The equation of a line is given by y = mx + c, where m = slope or gradient and c is intercept on y - axis. Given in this question, m = -5 and c = 3. Subtituting this in the equation y = mx + c, we have y = -5x + 3, therefore, the equation of the line is y = -5x + 3 or y + 5x = 3

2) The equation of a line is given as y-y1 = m(x-x1), where x1 = 6, y1 = -4 and m = -1/3. The equation of the line is y - -4 = -1/3(x - 6)

y+4 =-1/3(x-6)

3(y+4)= -1(x-6)

3y + 12 = -x+6

x+3y=6-12

x+3y= -6, therefore the equation of the line is x+3y = -6

3) The equation is y-y1=m(x-x1), where m=(y2-y1)/(x2-x1)=

(2- -4)/(-2-0)=6/-2=-3

y- -4= -3(x-0)= -3x

y+4= -3x

y+3x= -4

4) y-y1=m(x-x1)

m=(2-1) /(-4- -6)=1/2

y-1=1/2(x- -6)

y-1=1/2(x+6)

2(y-1) = x+6

2y-2=x+6

2y-x =6+2=8 2y-x=8

5) The equation is with undefined slope passing through (2, 5) is

x-2=0

x=2