How to find slope of a line - SSAT Upper Level Quantitative

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Question

What is the slope of the given linear equation?

2x + 4y = -7

Answer

We can convert the given equation into slope-intercept form, y=mx+b, where m is the slope. We get y = (-1/2)x + (-7/2)

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Question

Find the slope of the line 6X – 2Y = 14

Answer

Put the equation in slope-intercept form:

y = mx + b

-2y = -6x +14

y = 3x – 7

The slope of the line is represented by M; therefore the slope of the line is 3.

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Question

What is the slope of the line:

$\frac{14}{3}x=\frac{1}{6}y-7$

Answer

First put the question in slope intercept form (y = mx + b):

–(1/6)y = –(14/3)x – 7 =>

y = 6(14/3)x – 7

y = 28x – 7.

The slope is 28.

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Question

If 2x – 4y = 10, what is the slope of the line?

Answer

First put the equation into slope-intercept form, solving for y: 2x – 4y = 10 → –4y = –2x + 10 → y = 1/2*x – 5/2. So the slope is 1/2.

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Question

What is the slope of the line with equation 4_x_ – 16_y_ = 24?

Answer

The equation of a line is:

y = mx + b, where m is the slope

4_x_ – 16_y_ = 24

–16_y_ = –4_x_ + 24

y = (–4_x_)/(–16) + 24/(–16)

y = (1/4)x – 1.5

Slope = 1/4

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Question

Find the slope of the line that passes through the points $(2, -3)\text{ and }(-3, -3)$

Answer

Use the following formula to find the slope:

$\text{Slope}=\frac{y_2-y_1}{x_2-x_1}$

$\text{Slope}=\frac{-3-(-3)}{-3-2}=\frac{0}{-5}=0$

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Question

What is the slope of line 3 = 8y - 4x?

Answer

Solve equation for y. y=mx+b, where m is the slope

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Question

What is the slope of a line which passes through coordinates $\dpi{100} \small (3,7)$ and $\dpi{100} \small (4,12)$ ?

Answer

Slope is found by dividing the difference in the $\dpi{100} \small y$ -coordinates by the difference in the $\dpi{100} \small x$ -coordinates.

$\dpi{100} \small \frac{(12-7)}{(4-3)}=\frac{5}{1}=5$

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Question

What is the slope of a line that passes though the coordinates $(5,2)$ and $(3,1)$ ?

Answer

The slope is equal to the difference between the y-coordinates divided by the difference between the x-coordinates.

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

Use the give points in this formula to calculate the slope.

$m=\frac{1-2}{3-5}=\frac{-1}{-2}=\frac{1}{2}$

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Question

What is the slope of the line represented by the equation $6y-16x=7$ ?

Answer

To rearrange the equation into a $y=mx+b$ format, you want to isolate the $y$ so that it is the sole variable, without a coefficient, on one side of the equation.

First, add $11x$ to both sides to get $6y=7+16x$ .

Then, divide both sides by 6 to get $y=\frac{7+16x}{6}$ .

If you divide each part of the numerator by 6, you get $y=\frac{7}{6}+\frac{16x}{6}$ . This is in a $y=b+mx$ form, and the $m$ is equal to $\frac{16}{6}$ , which is reduced down to $\frac{8}{3}$ for the correct answer.

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Question

What is the slope of a line running through points and ?

Answer

The slope is equal to the difference between the y-coordinates divided by the difference between the x-coordinates.

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

Use the give points in this formula to calculate the slope.

$m=\frac{3-(-4)}{7-8}=\frac{7}{-1}=-7$

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Question

One end of a board that is four feet long is on the ground. The other end is balanced on a box that is one foot tall, creating a slope. What is the slope of the board?

Answer

The slope of a line is equal to $\frac{rise}{run}$ .

Given that the box is one foot tall, the rise will be equal to "1."

Given that the board is four feet long, the run will be equal to "4."

Therefore, the slope is equal to $\frac{rise}{run}=\frac{1}{4}$ .

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Question

A line is given with the equation . What is the slope of this line?

Answer

To find the slope, put the equation in form.

Since , that must be the slope of the line.

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Question

A line goes passes through the points $\left(-\frac{1}{2}, 5\right)\text{ and }\left(\frac{3}{2}, -1\right)$ . What is the slope of this line?

Answer

Use the following formula to find the slope of a line:

$\text{Slope}=\frac{y_2-y_1}{x_2-x_1}$

The slope of this line would be

$\frac{-1-5}{\frac{3}{2}-(-\frac{1}{2})}=\frac{-6}{2}=-3$

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Question

A line has the equation . What is the slope of the line?

Answer

Change the equation into the more familiar form. The value of will be the slope.

$y=\frac{8}{7}x-2$

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Question

What is the slope of a line that passes through the points $(15, -2)\text{ and }(-16, 20)$ ?

Answer

Use the following formula to find the slope:

$\text{Slope}=\frac{y_2-y_1}{x_2-x_1}$

Plug in the given points to find the slope.

$Slope=\frac{20-(-2)}{-16-15}=-\frac{22}{31}$

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Question

Find the slope of the line that goes through the points $(7, 15)\text{ and }(-3, -12)$

Answer

Use the following formula to find the slope:

$\text{Slope}=\frac{y_2-y_1}{x_2-x_1}$

Plug in the given points to find the slope.

$\text{Slope}=\frac{-12-15}{-3-7}=\frac{-27}{-10}=\frac{27}{10}$

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Question

Find the slope of the line that passes through the points $\left(\frac{1}{3}, -\frac{4}{5}\right)$ and $\left ( -6,10\right )$ .

Answer

Use the following formula to find the slope:

$\text{Slope}=\frac{y_2-y_1}{x_2-x_1}$

Plug in the given points to find the slope.

$\text{Slope}=\frac{10-(-\frac{4}{5})}{-6-\frac{1}{3}}=\frac{\frac{54}{5}}{-\frac{19}{3}}=-\frac{162}{95}$

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Question

Find the slope of the line that passes through the points $(-9, 2)\text{ and }(-2, -2)$

Answer

Use the following formula to find the slope:

$\text{Slope}=\frac{y_2-y_1}{x_2-x_1}$

$\text{Slope}=\frac{-2-2}{-2-(-9)}=-\frac{4}{7}$

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Question

Find the slope of the line that passes through the points $(-6, 2)\text{ and }(4,-4)$

Answer

Use the following formula to find the slope:

$\text{Slope}=\frac{y_2-y_1}{x_2-x_1}$

$\text{Slope}=\frac{-4-2}{4-(-6)}=\frac{-6}{10}=-\frac{3}{5}$

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