m is the slope.
b is the y-intercept.
given two points (x1,y1) and (x2,y1), the slope is equal to (y2-y1) / (x2-x1).
once you know the slope, you can use one of the points to find the y-intercept.
either one will do.
both will give you the same answer.
since the y-intercept is the value of y when x = 0, if one of the points is already at x = 0, then you already have your y-intercept.
#1 The first line: (0, 3) & (-4, 0)
slope = (y2-y1) / (x2-x1)
y2 = 0
y1 = 3
x2 = -4
x1 = 0
slope = (0-3) / (-4-0) = -3/-4 = 3/4
y-intercept = (0,3)
y = mx + b becomes y = 3/4*x + 3
Options:
A) y = (3/4)x + 3
B) y = (4/3)x + 3
C) y = (-4/3)x + 3
D) y = (-3/4)x + 3
selection A is your answer.
the graph of your equation is shown below:
#2 The second line: (-2, 2) & (2, -3)
y2 = -3
y1 = 2
x2 = 2
x1 = -2
slope = (-3-2) / (2-(-2)) = -5/4
y = mx + b becomes y = -5/4*x + b, where b is the y-intercept.
use x1,y1 as a point.
x1,y1 = (-2,2)
replace y with 2 and replace x with -2 to get:
y = -5/4*x + b becomes 2 = -5/4*(-2) + b
simplify to get 2 = 10/4 + b
subtract 10/4 from both sides of the equation to get b = 2 - 10/4 = 8/4 - 10/4 = -2/4
y = mx + b becomes:
y = -5/4*x - 1/2
Options:
A) y = (-3/2)x + 1/2
B) y = (3/2)x - 1/2
C) y = (3/2)x + 1/2
D) y = (-3/2)x - 1/2
none of the selections are the answer because the slope is -5/4 and not any combination of 3/2.
i was able to get the line correct and the points you referenced are on that line so i believe my answer is correct even though none of your selections match it.
here's a graph of my equation for your second problem.
i took the extra step to graph all of your the selections for the second problem.
none of them passed through the required points.
check your second problem to make sure you copied it correctly.