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

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

Point-Slope:
`y+4=-(1)/(2)(x+3)`

Slope-Intercept:
`y=-(1)/(2)x-(11)/(2)`

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)=-(1)/(2)(x- (-3))`

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

`y=-(1)/(2)x-(11)/(2)`