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Example Questions
Example Question #1 : How To Find The Equation Of A Line
What is the equation of the straight line passing through (–2, 5) with an x-intercept of 3?
y = –x – 3
y = –5x – 3
y = –x + 3
y = –5x + 3
y = –x + 3
First you must figure out what point has an x-intercept of 3. This means the line crosses the x-axis at 3 and has no rise or fall on the y-axis which is equivalent to (3, 0). Now you use the formula (y2 – y1)/(x2 – x1) to determine the slope of the line which is (5 – 0)/(–2 – 3) or –1. Now substitute a point known on the line (such as (–2, 5) or (3, 0)) to determine the y-intercept of the equation y = –x + b. b = 3 so the entire equation is y = –x + 3.
Example Question #1 : How To Find The Equation Of A Line
What is the equation of the line passing through (–1,5) and the upper-right corner of a square with a center at the origin and a perimeter of 22?
y = (–3/5)x + 28/5
y = (–3/5)x + 22/5
y = –x + 5
y = (3/5)x + 22/5
y = (–1/5)x + 2.75
y = (–3/5)x + 22/5
If the square has a perimeter of 22, each side is 22/4 or 5.5. This means that the upper-right corner is (2.75, 2.75)—remember that each side will be "split in half" by the x and y axes.
Using the two points we have, we can ascertain our line's equation by using the point-slope formula. Let us first get our slope:
m = rise/run = (2.75 – 5)/(2.75 + 1) = –2.25/3.75 = –(9/4)/(15/4) = –9/15 = –3/5.
The point-slope form is: y – y0 = m(x – x0). Based on our data this is: y – 5 = (–3/5)(x + 1); Simplifying, we get: y = (–3/5)x – (3/5) + 5; y = (–3/5)x + 22/5
Example Question #1 : How To Find The Equation Of A Line
What is the equation of a line passing through the points and
?
Based on the information provided, you can find the slope of this line easily. From that, you can use the point-slope form of the equation of a line to compute the line's full equation. The slope is merely:
Now, for a point and a slope
, the point-slope form of a line is:
Let's use for our point
This gives us:
Now, distribute and solve for :
Example Question #4 : How To Find The Equation Of A Line
What is the equation of a line passing through the two points and
?
Based on the information provided, you can find the slope of this line easily. From that, you can use the point-slope form of the equation of a line to compute the line's full equation. The slope is merely:
Now, for a point and a slope
, the point-slope form of a line is:
Let's use for our point
This gives us:
Now, distribute and solve for :
Example Question #5 : How To Find The Equation Of A Line
What is the equation of a line passing through with a
-intercept of
?
Based on the information that you have been provided, you can quickly find the slope of your line. Since the y-intercept is , you know that the line contains the point
. Therefore, the slope of the line is found:
Based on this information, you can use the standard slope-intercept form to find your equation:
, where
and
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.
Example Question #1 : Lines
Which line passes through the points (0, 6) and (4, 0)?
y = –3/2 – 3
y = 1/5x + 3
y = –3/2x + 6
y = 2/3x –6
y = 2/3 + 5
y = –3/2x + 6
P1 (0, 6) and P2 (4, 0)
First, calculate the slope: m = rise ÷ run = (y2 – y1)/(x2 – x1), so m = –3/2
Second, plug the slope and one point into the slope-intercept formula:
y = mx + b, so 0 = –3/2(4) + b and b = 6
Thus, y = –3/2x + 6
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
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