All ACT Math Resources
Example Questions
Example Question #101 : Lines
What line goes through the points (1, 3) and (3, 6)?
2x – 3y = 5
4x – 5y = 4
–3x + 2y = 3
3x + 5y = 2
–2x + 2y = 3
–3x + 2y = 3
If P1(1, 3) and P2(3, 6), then calculate the slope by m = rise/run = (y2 – y1)/(x2 – x1) = 3/2
Use the slope and one point to calculate the intercept using y = mx + b
Then convert the slope-intercept form into standard form.
Example Question #101 : Algebra
What is the slope-intercept form of ?
The slope intercept form states that . In order to convert the equation to the slope intercept form, isolate
on the left side:
Example Question #1 : How To Find The Equation Of A Line
A line is defined by the following equation:
What is the slope of that line?
The equation of a line is
y=mx + b where m is the slope
Rearrange the equation to match this:
7x + 28y = 84
28y = -7x + 84
y = -(7/28)x + 84/28
y = -(1/4)x + 3
m = -1/4
Example Question #1 : Lines
If the coordinates (3, 14) and (–5, 15) are on the same line, what is the equation of the line?
First solve for the slope of the line, m using y=mx+b
m = (y2 – y1) / (x2 – x1)
= (15 – 14) / (–5 –3)
= (1 )/( –8)
=–1/8
y = –(1/8)x + b
Now, choose one of the coordinates and solve for b:
14 = –(1/8)3 + b
14 = –3/8 + b
b = 14 + (3/8)
b = 14.375
y = –(1/8)x + 14.375
Example Question #1 : Coordinate Geometry
What is the equation of a line that passes through coordinates and
?
Our first step will be to determing the slope of the line that connects the given points.
Our slope will be . Using slope-intercept form, our equation will be
. Use one of the give points in this equation to solve for the y-intercept. We will use
.
Now that we know the y-intercept, we can plug it back into the slope-intercept formula with the slope that we found earlier.
This is our final answer.
Example Question #251 : Geometry
Which of the following equations does NOT represent a line?
The answer is .
A line can only be represented in the form or
, for appropriate constants
,
, and
. A graph must have an equation that can be put into one of these forms to be a line.
represents a parabola, not a line. Lines will never contain an
term.
Example Question #61 : Coordinate Geometry
Let y = 3x – 6.
At what point does the line above intersect the following:
They do not intersect
(–3,–3)
(0,–1)
(–5,6)
They intersect at all points
They intersect at all points
If we rearrange the second equation it is the same as the first equation. They are the same line.
Example Question #1 : How To Find The Equation Of A Line
Which of the following is the equation of a line between the points and
?
Since you have y-intercept, this is very easy. You merely need to find the slope. Then you can use the form to find one version of the line.
The slope is:
Thus, for the points and
, it is:
Thus, one form of our line is:
If you move the to the left side, you get:
, which is one of your options.
Example Question #2 : How To Find The Equation Of A Line
What is an equation of the line going through points and
?
If you have two points, you can always use the point-slope form of a line to find your equation. Recall that this is:
You first need to find the slope, though. Recall that this is:
For the points and
, it is:
Thus, you can write the equation using either point:
Now, notice that one of the options is:
This is merely a multiple of the equation we found, so it is fine!
Example Question #51 : Geometry
Given the graph of the line below, find the equation of the line.
To solve this question, you could use two points such as (1.2,0) and (0,-4) to calculate the slope which is 10/3 and then read the y-intercept off the graph, which is -4.
Certified Tutor
Certified Tutor
All ACT Math Resources
![Learning Tools by Varsity Tutors](https://vt-vtwa-app-assets.varsitytutors.com/assets/problems/og_image_practice_problems-9cd7cd1b01009043c4576617bc620d0d5f9d58294f59b6d6556fd8365f7440cf.jpg)