Question

A line passes through the points (–3, –4) and (6, 2). What is the x-intercept of this line? –3 A coordinate plane. What is the x-intercept of this line?

Answer 1

Answer:

x intercept is -3

Step-by-step explanation:

We need to find the equation for the line

First we find the slope

m = (y2-y1)/(x2-x1)

    = (2- -4)/(6- -3)

    = (2+4)/(6+3)

    =6/9

    = 2/3

The we can write the equation

y= mx+b

y = 2/3x +b

We can substitute in (6,2)

2 = 2/3(6) +b

2 =4+b

Subtract 4 from each side

2-4 =b

b =-2

y = 2/3 x-2

We want to find the x intercept, so set y =0 and solve for x

0 = 2/3x -2

Add 2 to each side

0-2 = 2/3x

Multiply each side by 3/2 to isolate x

-2 *3/2 = 2/3x * 3/2

-3 =x

The x intercept is -3

Answer 2

Answer:

(3,0)

Step-by-step explanation:

Slope: (2 - -4)/(6 - -3)

= 6/9 = 2/3

y = (⅔)x + c

2 = (⅔)6 + c

c = 2 - 4

c = -2

y = (⅔)x - 2

(⅔)x = 2

x = 2 × 3/2 = 3