Two lines or equations are described in each part. Decide whether each system has one solution, no solution, or infinitely many
solutions. Show your work AND explain your reasoning for each of your answers.
(a) Line a has a rate of change of 7.
Line b has a rate of change of -7
(b) 2x + 3y = 5.5
4x + 6y = 11
(c) These two graphed lines:
(d) Line c and line d are parallel.
(a) Line a has a rate of change of 7.
Line b has a rate of change of -7
(b) 2x + 3y = 5.5
4x + 6y = 11
(c) These two graphed lines:
(d) Line c and line d are parallel.
1 answer:
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y = mx + b
"m" is the slope, "b" is the y-intercept (the y value when x = 0)
To find the slope, you can use the slope formula and plug in the two points:
(3,63) = (x₁ , y₁)
(5,107) = (x₂, y₂)
m = 22
Now that you know m = 22, plug it into the equation:
y = mx + b
y = 22x + b
To find "b", plug in one of the points into the equation (I will do both points)
(3,63)
y = 22x + b
63 = 22(3) + b
63 = 66 + b Subtract 66 on both sides
-3 = b
(5,107)
y = 22x + b
107 = 22(5) + b
107 = 110 + b Subtract 110 on both sides
-3 = b
y = 22x - 3