Write an equation with the given slope that passes through the given point. m=-1/2;(-4,-1) m=5;(2,8)

Question

I need help and don't understand it.

Answer 1

Use the equation format y = mx + b, where x and y are variables, m is the slope, and b is the y-intercept.

Equations in this format describe the relationship between any x-value with its corresponding y-value in a point (x,y). When we know m, and we know a pair of coordinates x and y, we can solve for b.

part a)

given slope is m = -1/2

given point is (-4,-1)

m = -1/2, x = -4, y = -1

plug in m,x,and y to solve for b

y = mx+b

(-1) = (-1/2)(-4) + b by plugging in values for m,x,b

(-1) = 2 + b by simplifying (-1/2)(-4) = 2

-3 = b by subtracting 2 from both sides

now that we know both m and b, we can write our equation:

y = (-1/2)x - 3

part b)

Same process, but now we have m = 5 and the given point (2,8)

using y = mx + b,

plug in m = 5, x = 2, and y = 8

8 = (5)(2) + b

8 = 10 + b subtract 10 from both sides

-2 = b

now, with m = 5 and b = -2, we have the equation

y = 5x - 2

Answer 2

In a problem like this you always first want to look at what you are given. Here you are given the point and slope of the line. With this information you can create the equation of the line by using point-slope form.

The equation goes:

y - y1 = m (x-x1) where (x1, y1) is the point

For this problem it would be:

y- (-1) = -1/2(x - -4) this then simplifies to

y+1 = -1/2(x+4) distributing the -1/2 gives

y+1 = -1/2x -2 finally you can subtract 1 from both sides to turn the equation into slope-intercept form

y = -1/2x - 3