Question

Find an equation for the line that passes through point (-2,4) and (4,-5)
(Show Work)

Answer 1

`\Huge\boxed{\mathsf{Y=-(3)/(2)x+1}}}`

Explanation:

TO FIND:

The slope of (-2,4) and (4,-5).

TO SOLVE:

With slope-intercept form and slope formula.

SLOPE FORMULA:

`\displaystyle \mathsf{\Rightarrow (Y_2-Y_1)/(X_2-X_1)=(RISE)/(RUN)  }}`

SLOPE-INTERCEPT FORM:

`\displaystyle \mathsf{\Rightarrow Y=MX+B}}`

SOLUTIONS:

Y₂=(-5)

Y₁=4

X₂=4

X₁(-2)

Solve.

`\displaystyle \mathsf{((-5)-4)/(4-(-2))=((-5)-4)/(4+2)=(-9/3)/(6/3)=(-3)/(2)=-\Rightarrow (3)/(2)     }}`

Y-intercept is 1.

Y=-3/2x+1.

`\Large\boxed{\mathsf{Y=-(3)/(2)x+1 }}}`

The correct answer is y=-3/2x+1.

Answer 2

y=-9/6x+1

Explanation:

Slope=y2-y1/x2-x1

1) Find the slope of the line:

(-5-4)/(4+2)

2) Simplify:

m= -9/6

3) Now plug in the slope into point slope formula: (attached as picture)

(y-4)=-9/6(x+2)

4) Distribute -9/6 to x and 2:

y-4=-9/6x-3

5) Add 4 to both sides:

y=-9/6x+1