how to find the equation of a line with two points

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Given two points, (5, –8) (–2, 6), what is the equation of the line containing them both?

Possible Answers:

y = –2x + 2

y = (–2/7)x + 8

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.

$slope=\frac{y_2-y_1}{x_2-x_1}$

$slope=\frac{-8-6}{5-(-2)}=\frac{-8-6}{5+2}=\frac{-14}{7}=-2$

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

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

Possible Answers:

y = –5x + 3

y = (3/5)x + 2

y = 3x + 5

y = 5x – 3

y = 3x – 5

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

A line contains the points (8, 3) and (-4, 9). What is the equation of the line?

Correct answer:

$y=-\frac{1}{2}x+7$

Explanation:

y=mx+b is the slope-intercept form of the equation of a line.

Slope is equal to $\frac{rise}{run}$ between points, or $\frac{6}{-12}$ .

So $m=-\frac{1}{2}$ .

At point (8, 3 ) the equation becomes

$3=-\frac{1}{2}\cdot 8+b\rightarrow 3=-4+b$

So b=7

Given two points $\left ( 1,5 \right )$ and $\left ( 0,2 \right )$ , find the equation of a line that passes through the point $\left ( -3,-5 \right )$ and is parallel to the line passing through points and .

Correct answer:

3x-y=-4

Explanation:

The slope of the line passing through points and can be computed as follows:

$Slope = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{5-2}{1-0}=3$

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:

$y-y_{1}=m(x-x_{1})$ , where is the slope and $\left ( x_{1},y_{1} \right )$ is the point the line passes through.

y-(-5)=3(x-(-3))

y+5-3(x+3)

y+5=3x+9

After rearranging, this becomes 3x-y=-4

Find the equation, in y=mx+b form, of the line that contains the points (2,10) and (-4,13) .

Correct answer:

$y=-\frac{1}{2}x+11$

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

Question_5

Correct answer:

y=3x+4

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.

$m=\frac{y_{2}-y_1}{x_2-x_1}=\frac{7-4}{1-0}=\frac{3}{1}=3$

Next, using the slope and any point on the line, calculate the y-intercept, . We will use the first point.

y=mx+b

4=3(0)+b

4=b

The correct equation in slope-intercept form is y=3x+4 .

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

Correct answer:

y=2x-12

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, ?

Correct answer:

p(x)=2.176x-4,303.07

Explanation:

We can treat the price of the stock as the value and the year as the value, making any points take the form (year, price) , or (x,p) . This question is asking for the line that includes points (1990,27.17) and (2000,48.93) .

To find the equation, first, we need the slope.

$m= \frac{48.93-27.17}{2000-1990}= \frac{21.76}{10}=2.176$

Now use the point-slope formula with this slope and either point (we will choose the second).

y-48.93 = 2.176(x-2000)

y-48.93 = 2.176x-4352

y = 2.176x-4303.07

Which of these lines has a slope of 5 and a -intercept of 6?

Correct answer:

y=5x+6

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