All Algebra 1 Resources
Example Question #1 : How To Find The Equation Of A Line
Given two points, (5, –8) (–2, 6), what is the equation of the line containing them both?
y = –2x + 2
y = (–2/7)x + 8
y = 2x – 2
y = (2/7)x – 8
y = –2x + 2
First, you should plug the given points, (5, –8) (–2, 6), into the slope formula to find the slope of the line.
Then, plug the slope into the slope formula, y = mx + b, where m is the slope.
y = –2x + b
Plug in either one of the given points, (5, –8) or (–2, 6), into the equation to find the y-intercept (b).
6 = –2(–2) + b
6 = 4 + b
2 = b
Plug in both the slope and the y-intercept into slope intercept form.
y = –2x + 2
Example Question #2 : How To Find The Equation Of A Line
What is the equation of a line with slope of 3 and a y-intercept of –5?
y = (3/5)x + 2
y = 3x + 5
y = –5x + 3
y = 5x – 3
y = 3x – 5
y = 3x – 5
These lines are written in the form y = mx + b, where m is the slope and b is the y-intercept. We know from the question that our slope is 3 and our y-intercept is –5, so plugging these values in we get the equation of our line to be y = 3x – 5.
m = 3 and b = –5
Example Question #3 : How To Find The Equation Of A Line
A line contains the points (8, 3) and (-4, 9). What is the equation of the line?
is the slope-intercept form of the equation of a line.
Slope is equal to between points, or .
At point (8, 3 ) the equation becomes
Example Question #4 : How To Find The Equation Of A Line
Given two points and , find the equation of a line that passes through the point and is parallel to the line passing through points and .
The slope of the line passing through points and can be computed as follows:
Now, the new line, since it is parallel, will have the same slope. To find the equation of this new line, we use point-slope form:
, where is the slope and is the point the line passes through.
After rearranging, this becomes
Example Question #5 : How To Find The Equation Of A Line
Find the equation, in form, of the line that contains the points and .
When finding the equation of a line from some of its points, it's easiest to first find the line's slope, or .
To find slope, divide the difference in values by the difference in values. This gives us divided by , or .
Next, we just need to find , which is the line's -intercept. By plugging one of the points into the equation , we obtain a value of 11 and a final equation of
Example Question #6 : How To Find The Equation Of A Line
We can find the equation of th line in slope-intercept form by finding and .
First, calculate the slope, , for any two points. We will use the first two.
Next, using the slope and any point on the line, calculate the y-intercept, . We will use the first point.
The correct equation in slope-intercept form is .
Example Question #7 : How To Find The Equation Of A Line
What is the equation of a line with a slope of and a -intercept of ?
None of the above
When a line is in the format, the is its slope and the is its -intercept. In this case, the equation with a slope of and a -intercept of is .
Example Question #8 : How To Find The Equation Of A Line
In 1990, the value of a share of stock in General Vortex was $27.17. In 2000, the value was $48.93. If the value of the stock rose at a generally linear rate between those two years, which of the following equations most closely models the price of the stock, , as a function of the year, ?
We can treat the price of the stock as the value and the year as the value, making any points take the form , or . This question is asking for the line that includes points and .
To find the equation, first, we need the slope.
Now use the point-slope formula with this slope and either point (we will choose the second).
Example Question #9 : How To Find The Equation Of A Line
Example Question #10 : How To Find The Equation Of A Line
Which of these lines has a slope of 5 and a -intercept of 6?
When an equation is in the form, the indicates its slope while the indicates its -intercept. In this case, we are looking for a line with a of 5 and a of 6, or .