# Algebra 1 : How to find the equation of a line

## Example Questions

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### 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?

No Solution

y = (–2/7)x + 8

y = –2x + 2

y = (2/7)x – 8

y = 2x – 2

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 : Slope And Line Equations

What is the equation of a line with slope of 3 and a y-intercept of –5?

y = 5x – 3

y = (3/5)x + 2

y = 3x – 5

y = 3x + 5

y = –5x + 3

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 #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?

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 #1 : 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 .

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 .

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 #1 : How To Find The Equation Of A Line

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

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 #2 : 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

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 #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, ?

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).

Explanation:

### 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?