Question

Use y = mx + b to determine the equation of a line with a slope -5, passing through the point (-2,4).

Answer 1

`y=-5x-6`

Explanation:

Hi there!

In
`y=mx+b`, m is the slope of the line and b is the y-intercept (the value of y when x is 0). y and x remain the same but m and b are replaced with numbers.

Given that the slope is -5, plug it into
`y=mx+b`:

`y=-5x+b`

Now, to solve for b, plug in the given point (-2,4):

`4=-5(-2)+b\\4=10+b`

Subtract 10 from both sides to isolate b:

`4-10=10+b-10\\-6=b`

Therefore, the y-intercept of this line is -6. Plug this back into
`y=-5x+b` as b:

`y=-5x-6`

I hope this helps!