Question

Write an equation in point slope and slope intercept form of a line that passes through the given point and has the given slope m.(If possible please show work)

Answer 1

Answer: Point slope form   y+4= -1/2(x+3)  

Slope intercept form: y=-1/2x -11/2

Step-by-step explanation:

(-3,-4) : m= -1/2  

So we know the slope and to write it in point slope form it will be like ,

y- b = m(x-a)   Where b is the y value and a is the x value  and m in this case is the slope .

y- (-4) = -1/2 ( x-(-3)   which reduces to  y+4= -1/2(x+3)

Now to write it in slope intercept form  it will be  like y=mx+b and we kow htat m is the slope but we do not know b the y-intercept. But using the given coordinates we could plot it into the formula and solve for b.

y = mx +b

We  know that y is -4  

We know that m is -1/2  

we know that x is  -3  

so  -4 = -1/2(-3) + B

    -4  = 3/2 + b

   -3/2    -3/2

  b= -11/2  

We know now that the y intercept is -11/2 so we could write  it in slope intercept form.

y= -1/2x - 11/2

Answer 2

Answer:

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

Slope-Intercept: $y=-\frac{1}{2}x-\frac{11}{2}$

Step-by-step explanation:

The point-slope formula is $y-y_{1}=m(x-x_{1} )$. The slope-intercept formula is $y=mx+b$. Since we are given the point and slope, we can directly plug it into the point-slope formula.

Point-Slope

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

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

To find the slope-intercept form, we can manipulate the point-slope form to get the slope-intercept form.

Slope-Intercept

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

$y=-\frac{1}{2}x-\frac{11}{2}$