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

Answer:

1

Step-by-step explanation:

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

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

    $= > Equation: (y-4)=-\frac{3}{2}(x+2)$

To convert the equation to slope-intercept form:

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

      $y= -\frac{3}{2}(x+2)+4\\ y=-\frac{3}{2} x-3+4\\y=-\frac{3}{2}x+1$

Answer: $y = -\frac{3}{2}x+1$

Hope that helps!