Algebra 1 : Equations of Lines

Study concepts, example questions & explanations for Algebra 1

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Example Questions

Example Question #91 : Perpendicular Lines

Suppose a line has an x-intercept of one and a y-intercept of two. What is the equation of the perpendicular line which pass through the point ?

Possible Answers:

Correct answer:

Explanation:

Write the points that correspond to the x and y-intercepts given in the problem.

X-intercept of one: 

Y-intercept of two: 

Find the slope of this line connected with these points.

The slope is negative two. The slope of the perpendicular line is the negative reciprocal of this slope.

Write the slope-intercept form.

Substitute the perpendicular slope with the point that this line will pass through.

Solve for the y-intercept, .

Subtract nine halves on both sides.

Simplify both sides.

With the perpendicular slope and the y-intercept, write the equation of the line.

The answer is:

Example Question #331 : Functions And Lines

What is the slope of a line perpendicular to the line with the following equation?

Possible Answers:

Answer cannot be determined from this information.

Correct answer:

Explanation:

Step 1: get the line into y = mx +b format to find the slope m:

Next, we need to remember that perpendicular lines have slopes that are negative reciprocals. Find the negative reciprocal of :

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?

Possible Answers:

y = (2/7)x – 8

y = 2x – 2

y = –2x + 2

y = (–2/7)x + 8

No Solution

Correct answer:

y = –2x + 2

Explanation:

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 #1 : 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? 

Possible Answers:

y = –5x + 3

y = 3x + 5

y = 5x – 3

y = 3x – 5

y = (3/5)x + 2

Correct answer:

y = 3x – 5

Explanation:

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 #1 : 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?

Possible Answers:

Correct answer:

Explanation:

is the slope-intercept form of the equation of a line.

Slope  is equal to  between points, or .

So .

At point (8, 3 ) the equation becomes

So

Example Question #2 : 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 .

Possible Answers:

Correct answer:

Explanation:

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 #1 : How To Find The Equation Of A Line

Find the equation, in  form, of the line that contains the points  and .

Possible Answers:

Correct answer:

Explanation:

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 #4 : How To Find The Equation Of A Line

What is the equation of a straight line that connects the points indicated in the table?

Question_5

Possible Answers:

Correct answer:

Explanation:

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 #3 : How To Find The Equation Of A Line

What is the equation of a line with a slope of  and a -intercept of ?

Possible Answers:

None of the above

Correct answer:

Explanation:

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 #1 : 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, ?

Possible Answers:

Correct answer:

Explanation:

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).

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