Question

Please please help me 30 points if you can I need the answer I know how to do it I just suck with the fractions

Answer 1

1

Explanation:

`\text{Given that,}~ (x_1,y_1) = (-2,4)~ \text{and}~ \text{slope,}~ m = -\frac 32\\ \\\text{Equation of line,}~\\\\~~~~~~~y -y_1 = m(x-x_1)\\\\\implies y -4 =-\frac 32(x+2)\\\\\implies y-4 =-\frac 32x - 3\\\\\implies y = -\frac 32x -3 +4\\\\\implies y = -\frac 32x +1`

Answer 2

The current equation of the perpendicular line;

⇒ is the slope-intercept form:
`y= mx + b`

• m: is the coefficient in front of the x, which is also the slope's value
• b: y-intercept of the function

Now for the point-slope form, we need a point on the line and the slope of the line:

⇒ we have

• slope = -3/2
• point: (-2,4)

Since this is the point-slope form:
`(y-y_1)=m(x-x_1)`

⇒ where the (x₁,y₁) is the point on the line and m is the slope

`= > Equation: (y-4)=-(3)/(2)(x+2)`

To convert the equation to slope-intercept form:

⇒ must isolate 'y' to one side and everything to the other side

`y= -(3)/(2)(x+2)+4\\ y=-(3)/(2) x-3+4\\y=-(3)/(2)x+1`

Answer:
`y = -(3)/(2)x+1`

Hope that helps!