Algebra Question i need ASAP

Question

1) Write a equation in slope intercept form for a line that passes through (4,2) and has a slope of -1/4.

2) write an equation in slope intercept form for a lawn that passes through the points (3,6) and (2,3).

Answer 1

Slope intercept form: y = mx + b

1) You're given a point and the slope, so you can solve for the y-intercept (b):

y = mx + b

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

2 = -1 + b

+1 +1

3 = b

Now that you know the slope and y-intercept, you can write the equation:

y = (-1/4)x + 3

2) You're given two points, so first you have to find the slope:

m = y₂ - y₁

x₂ - x₁

m = 3 - 6 = -3 = 3

2 - 3 -1

Use either one of the points and the slope found above to solve for the y-intercept (as done in part 1):

Choosing (2,3)

y = mx + b

3 = 3(2) + b

3 = 6 + b

-6 -6

-3 = b

Write equation using slope and y-intercept:

y = 3x - 3