Question

PLZZZ  HELP WITH 2 PROBLEMS

Find x- and y-intercepts. Write ordered pairs representing the points where the line crosses the axes. y= 1/3 x− 2/3

Given the graph of a line y=−x.Write an equation of a line which is perpendicular and goes through the point (8,2).

Answer 1

Answer:

1. (0, -2/3), (2, 0)

2. y = x-6

Step-by-step explanation:

1. Since the equation is in slope-intercept form, you know the y-intercept is -2/3. The x-coordinate there is 0, so the ordered pair is (0, -2/3).

Substituting y=0 into the equation gives the value of the x-intercept.

... 0 = 1/3x -2/3

... 0 = x - 2 . . . . . multiply by 3

... 2 = x . . . . . . . . add 2

The x-intercept is (2, 0).

2. The given line has slope -1, so the perpendicular line has a slope that is the negative reciprocal of that: -1/-1 = 1. Then the point-slope equation of the line can be written ...

... y = 1(x -8) +2

... y = x - 6 . . . . simplify

Answer 2

(1)

to find the intercepts

• let x = 0, in the equation for y-intercept

• let y = 0, in the equation for x-intercept

x = 0 : y = - $\frac{2}{3}$ → (0, - $\frac{2}{3}$) ← y-intercept

y = 0 : $\frac{1}{3}$ x - $\frac{2}{3}$ = 0 ( multiply by 3 )

x - 2 = 0 → x = 2 → (2, 0 ) ← x- intercept

(2)

the equation of a line in slope-intercept form is

y = mx + c ( m is the slope and c the y-intercept )

y = - x is in this form with slope m = - 1

the slope of a perpendicular line = - $\frac{1}{m}$ = 1

the partial equation of the perpendicular line is

y = x + c

to find c substitute (8, 2 ) into the partial equation

2 = 8 + c → c = 2 - 8 = - 6

y = x - 6 ← equation of perpendicular line