Question

A line passes through (1, –5) and (–3, 7). a. Write an equation for the line in point-slope form. b. Rewrite the equation in slope-intercept form

Answer 1

y-y1 x-x1 -------- = ------- y2-y1 x2-x1
y-(-5) x-1 ------- = ---- 7-(-5) -3-1
y+5*(-4)=12*(x-1) -4y-20=12x-12 12x+4y+8=0 /4 3x+y+2=0


why: To form an linear equation for a line, you must remember 2 things
****First find its gradient, second, find the y-intercept.
General equation for a line: y = mx + c, where m = gradient, and c = y-intercept.
Gradient, m = {7 - (-5)} / {(-3) - 1} = - 3
To find the y-intercept, you must use one of the point (-3, 7) or (1, -5) and substitute the value of x and y from the coordinate u choose into the general equation y = mx + c.
I choose (1, -5), so -5 = -3(1) + c -5 = -3 + c -5 + 3 = c -2 = c
Thus,
the equation in slope-intercept form is y = -3x - 2.
the equation in standard form is y + 3x + 2 = 0
the equation in point-slope form is y + 3x = -2 divide both sides with -2 y / (-2) + 3x / (-2) = -2 / -2 - y / 2 - x / (2/3) = 1

Answer 2

(a) y-(-5)= -3(x-1)

(b) y = -3x -2

Explanation:

Point slope form is

y-y1= m(x-x1)

Where m is the slope

slope formula is
`(y_2-y_1)/(x_2-x_1)`

(x1,y1) is (1, –5) and (x2,y2) is (–3, 7)

`m=(7-(-5))/((-3)-1)`

`m=(-12)/(4)=-3`

use m=-3 and point (1,-5)

y-y1= m(x-x1)

(a) Point - slope form is

y-(-5)= -3(x-1)

(b) Rewrite the equation in slope-intercept form, solve for y

y+5 = -3x + 3

Subtract 5 on both sides

y = -3x -2