IXL help
S.8 Slope-intercept form: write an equation
S.9
Linear equations: solve for y
y
Here is how I got the answer:
I know the equation of a line is 𝑦 = 𝑚𝑥 + 𝑏, so my goal was to start out with the given equation and rearrange it
so it looked like 𝑦 = 𝑚𝑥 + 𝑏 form of the line.
S.10
Linear function word problems
How I solved the problem:
Step 1: First I need to think of my two variables (dependant and independent). In this case, I will let t be the total
number of quizzes, and I will let w be the total number of weeks.
Step 2: Now I can write an equation that will represent the scenario
Step 3: Now I can sub in for my known variables and solve for my unknown variable. In this case, if I want to know
how many quizzes Kendall will have in total after 8 weeks of school, I would sub in 8 for w, and solve for t.
𝑡 = 1𝑤 + 1
𝑡 = 1(8) + 1
𝑡=9
S.11
Write equations in standard form
How I solved this problem:
I know the equation of a line in standard form is 𝐴𝑥 + 𝐵𝑦 = 0, where A must be greater than 0, and B cannot be 0.
So, I took my original equation and rearranged it using algebra until it took standard form.
S.12 Standard Form: Find the x and y intercepts
I know at the x intercept, y = 0. I know at the y intercept, x = 0. So, if I need to find the x intercept, I need to make
y = 0. I will then sub y = 0 into the given equation to solve for x.
𝑥 + 5𝑦 = 7
𝑥 + 5(0) = 7
𝑥=7
To graph a line, I need two points. In standard
form I will find the two intercepts to give
myself two points to graph.
I know at the x intercept, y = 0.
6𝑥 + 7𝑦 = 42
6𝑥 + 7(0) = 42
6𝑥 = 42
𝑥=
42
6
𝑥=7
So now I know one point (7,0)
Now….
I know at the y intercept, x = 0.
6𝑥 + 7𝑦 = 42
6(0) + 7𝑦 = 42
7𝑦 = 42
𝑦=
42
7
𝑦=6
So now I have another point (0,6). I can now
plot my two points and connect the line.
R.6. Identify Direct and Partial Variation
Direct Variation is when you have a line and it goes
through the origin. You can say that y varies directly with
x. In Direct variation, one variable is a constant multiple
of the other variable.
Partial Variation is when you have a line and id does not
go through the origin. Partial variation represents a
relationship between 2 variables in which one variable is
a constant multiple of the other, plus some constant.
Example:
Example
1
𝑦 = 3 𝑥 + 0 The 0 is the y intercept, indicating the line
passes through the origin (0,0)
Or
y = 10x + 20, where 10 is the rate of change, and 20 is
1
𝑦= 𝑥
the original constant variable.
3
Example from IXL:
To solve this problem, I first need to use the equation of a line and solve for m (the constant rate of change) but
subbing in the given values of x and y into the equation.
𝑦 = 𝑚𝑥 + 𝑏
12 = 𝑚(2) + 0
12
=𝑚
2
6=𝑚
Now I know the constant variable, or that y is a constant multiple of x.
The equation is 𝑦 = 6𝑥