Below is a selection of types of questions you could see on the LEAP 2025 test for Algebra I. Be sure to read the directions for each set of questions and the tips/hints provided to get you through.
This unit focuses on everything functions.
SLOPE
There are two different ways we can calculate the slope of a line depending on the data given.
GRAPH
When looking at a graph, in order to determine the slope, we pick two points. We count the vertical change and the horizontal change.
If a graph is moving up from left to right, the slope is positive.
If a graph is moving down from left tot right, the slope is negative.
POINTS
When given either two points or a table of points, we must use the formula that is change in y over change in x as shown below.
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1 point
1
Question 1
1.
What is the slope of the graph below?
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1 point
1
Question 2
2.
What is the slope of the graph below?
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1 point
1
Question 3
3.
What is the slope of the table below?
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1 point
1
Question 4
4.
Slope of a line passing through the points (1,2) and (3,5).
Not only do we have positive and negative slopes, we also have slopes that are 0 or undefined.
Positive Slope
Negative Slope
Undefined Slope
An undefined slope has an equation that is x = the value it passes through. For the picture above, the equation would be x = 2
0 Slope
A slope of 0 has an equation that is y = the value it passes through. For the picture above, the equation would be y = 3.
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1 point
1
Question 5
5.
Write an equation for the graph below.
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1 point
1
Question 6
6.
Write the equation for the graph shown below.
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1 point
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Question 7
7.
Write an equation for a graph with 0 slope that passes through the point (2,-3).
WRITING LINEAR FUNCTIONS
When writing linear functions, we need to break down what is a linear equation. The most basic formula we use to represent this is
where m represents the slope (rate of change) and b represent the starting value.
In a word problem, there are some key phrases that are used to lead us into understanding which values would represent a slope and which would represent the starting value. For example:
A plumber charges $50 to make a house call and he also charges $25 per hour for labor.
When reading this, we have two important values. Using logic, we know that know matter how many hours the plumber works it will cost $50. This would be our starting value.
The $25 per hour part is our slope. The key word that identifies this is "per."
So if I were to write the function with 25 as my slope and 50 as my starting value, it'd be
with f(x) representing the total amount the plumber would make after working x hours at this house.
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4 points
4
Question 8
8.
For each of the following, finish writing the formula based on the information given.
1.) Cynthia works at a carpentry shop for the week. She starts at $50 and earns $10 per hour. Let x represent the number of hours worked and f(x) represent the total money earned.
f(x) = _______ x + _______
2.) Timmy has 200 shells in his collection. He is removing shells from his collection at 5 per day. Let g(x) represent the number of shells remaining after x days.
g(x) = _______ x + _______
3.) Charles has $150 in his savings. He spends $3 each time he buys a burger from the local area. Let h(x) represent the total money remaining after x burgers purchased.
h(x) = _______ x + _______
4.) Juan earns $7 per hour plus $20 per week making picture frames. Let r(x) represent Juan's total earnings if he works x hours in one week.
r(x) = _______ x + _______
SLOPE-INTERCEPT FORM
The previous formula we used has a name and it is called slope-intercept form. This basic form that we use tell us two things about the data that accompanies it.
Remember, an equation is denoted with y and a function is f(x).
These are the two way you may see it and we are already familiar with the first one. Again, m stands for the slope (rate of change) and b stands for the starting value. The starting value is also the y-intercept of the graph. This is where the graph crosses the y-axis.
In order to put something in slope-intercept form, we need to know the above mentioned parts. That means we must determine the slope and intercept.
This is shown in the images on the right.
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1 point
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Question 9
9.
Write the slope-intercept form of the equation given a slope of 4/3 and a y-intercept of 3.
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1 point
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Question 10
10.
Write the slope-intercept form of the equation given a y-intercept of 1 and a slope of -1.
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1 point
1
Question 11
11.
Write the slope-intercept form of the equation for a line that passes through the points (-4,1) and (0,5).
PARALLEL LINES
Parallel lines are lines that have the same slope but different y-intercepts. We may be given a question where we are asked to determine the equation of a line that is parallel to another that passes through a specific point. Below is an example of a problem and how it is worked.
We determine the value of the new slope first which is the same value since parallel lines have the same slope. *Then we use the slope-intercept formula to find the new y-intercept by substituting the slope and the point the new line passes through. This will give us the new line's equation.
On Desmos
If you want to try these on desmos, you still have to know about the slopes of parallel lines. You can plot the point the new line passes through and use the slope to determine what the y-intercept would be.
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1 point
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Question 12
12.
Equation for a line parallel to
that passes through ( -1, -1)
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1 point
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Question 13
13.
Equation for a line parallel to
and passes through (2,4)
Perpendicular Lines
Perpendicular lines are worked almost like parallel lines except the slopes are different. They are opposite reciprocals. To get the opposite reciprocal, you will flip the positions of the numerator and denominator. This means that if the slope was 4, the perpendicular slope would be -1/4.
If the slope of the original line is -2, the perpendicular slope would be 1/2.
Below is an example of how it is worked to find the new equation of a perpendicular line that passes through a point.
You do the same steps as parallel lines. Substitute the new slope and the point the line passes through and solve for b.
On Desmos
If looking to do this on desmos, you work it like the parallel lines. Plot the new point the line passes through and use the new slope to find the y-intercept.
