GMAT Math : Calculating the slope of a line

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Example Question #92 : Coordinate Geometry

Fill in the circle with a number so that the graph of the resulting equation has slope $\frac{4}{5}$ :

$\bigcirc x+ 7y = 20$

Possible Answers:

$-\frac{35}{4}$

$\frac{5}{28}$

$\frac{4}{35}$

None of the other responses is correct.

$-\frac{28}{5}$

Correct answer:

$-\frac{28}{5}$

Explanation:

Let be that missing coefficient. Then the equation can be rewritten as

Ax+ 7y = 20

Put the equation in slope-intercept form:

7y = -Ax + 20

$\frac{7y }{7}=\frac{ -Ax + 20}{7}$

$y =- \frac{ A }{7}x+ \frac{ 20}{7}$

The coefficient of is the slope, so solve for in the equation

$- \frac{ A }{7} =\frac{4}{5}$

$- \frac{ A }{7} \cdot (-7)=\frac{4}{5} \cdot (-7)$

$A=-\frac{28}{5}$

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Example Question #93 : Coordinate Geometry

Fill in the circle with a number so that the graph of the resulting equation has slope 4:

$5 y = \bigcirc x + 4$

Possible Answers:

$\frac{4}{5}$

$\frac{5}{4}$

Correct answer:

Explanation:

Let be that missing coefficient. Then the equation can be rewritten as

5 y = Ax + 4

Put the equation in slope-intercept form:

$\frac{5 y}{5} =\frac{ Ax + 4}{5}$

$y = \frac{A}{5}x + \frac{4}{5}$

The coefficient of is the slope, so solve for in the equation

$\frac{A}{5} = 4$

$\frac{A}{5}\cdot 5 = 4 \cdot 5$

A = 20

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Example Question #94 : Coordinate Geometry

Examine these two equations.

5 x - 3 y = 9

$\square y = x + 7$

Write a number in the box so that the lines of the two equations will have the same slope.

Possible Answers:

$\frac{3}{5}$

$\frac{5}{9}$

$\frac{9}{5}$

$\frac{5}{3}$

Correct answer:

$\frac{3}{5}$

Explanation:

Write the first equation in slope-intercept form:

5 x - 3 y = 9

5 x - 3 y +3y - 9 = 9+3y - 9

3y = 5x-9

$\frac{3y}{3} = \frac{5x-9}{3}$

$y = \frac{5}{3}x - 3$

The coefficient of , which here is $\frac{5}{3}$ , is the slope of the line.

Now, let be the nuimber in the box, and rewrite the second equation as

A y = x + 7

Write in slope-intercept form:

$\frac{A y }{A}= \frac{x + 7}{A}$

$y = \frac{1}{A}x+\frac{7}{A}$

The slope is $\frac{1}{A}$ , which is set to $\frac{5}{3}$ :

$\frac{1}{A}= \frac{5}{3}$

$A= \frac{3}{5}$

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Example Question #11 : Calculating The Slope Of A Line

Fill in the circle with a number so that the graph of the resulting equation is a horizontal line:

$y = x + \bigcirc$

Possible Answers:

The graph cannot be a horizontal line no matter what number is written.

is the only number that works.

The graph is a horizontal line no matter what number is written.

Correct answer:

The graph cannot be a horizontal line no matter what number is written.

Explanation:

The equation of a horizontal line takes the form y = b for some value of . Regardless of what is written, the equation cannot take this form.

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Example Question #96 : Coordinate Geometry

Fill in the square and the circle with two numbers so that the line of resulting equation has slope $-\frac{3 }{5}$ :

$\square x + 4y = \bigcirc$

Possible Answers:

$-\frac{12}{5}$ in the square and $-\frac{3}{7}$ in the circle

None of the other responses is correct.

$\frac{20}{3}$ in the square and $\frac{3}{7}$ in the circle

$-\frac{20}{3}$ in the square and $-\frac{4}{7}$ in the circle

$\frac{12}{5}$ in the square and $\frac{4}{7}$ in the circle

Correct answer:

$\frac{12}{5}$ in the square and $\frac{4}{7}$ in the circle

Explanation:

Let and be those missing numbers. Then the equation can be rewritten as

A x + 4y = C

Put the equation in slope-intercept form:

4y =-Ax+ C

$\frac{4y}{4} =\frac{-Ax+ C}{4}$

$y =-\frac{A}{4}x + \frac{ C}{4}$

The coefficient of is the slope, so solve for in the equation

$-\frac{A}{4} = -\frac{3}{5}$

$-\frac{A}{4} \cdot (-4) = -\frac{3}{5} \cdot (-4)$

$A = \frac{12}{5}$

The number in the circle is irrelevant, so the correct choice is that $\frac{12}{5}$ goes in the square and $\frac{4}{7}$ goes in the circle.

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Example Question #691 : Geometry

Fill in the circle with a number so that the graph of the resulting equation has slope 4:

$y = 6x + \bigcirc$

Possible Answers:

$-\frac{3}{2}$

$\frac{3}{2}$

It is impossible to do this.

Correct answer:

It is impossible to do this.

Explanation:

Once a number is filled in, the equation will be in slope-intercept form

y = mx+b ,

so the coefficient of will be the slope of the line of the equation. Regardless of the number that is written in the circle, this coefficient, and the slope, will be 6, so the slope cannot be 4.

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Example Question #98 : Coordinate Geometry

Consider segment $\overline{JK}$ which passes through the points $\left ( 4,5\right )$ and $\left ( 144,75\right )$ .

What is the slope of $\overline{JK}$ ?

Possible Answers:

$\small \frac{3}{4}$

$\small 2$

$\small \frac{1}{2}$

$\small \frac{2}{3}$

$\small -\frac{1}{2}$

Correct answer:

$\small \frac{1}{2}$

Explanation:

Slope is found via:

$\small m=\frac{y'-y}{x'-x}$

Plug in and calculate:

$\small \small m=\frac{75-5}{144-4}=\frac{70}{140}=\frac{1}{2}$

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GMAT Math : Calculating the slope of a line

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #92 : Coordinate Geometry

Example Question #93 : Coordinate Geometry

Example Question #94 : Coordinate Geometry

Example Question #11 : Calculating The Slope Of A Line

Example Question #96 : Coordinate Geometry

Example Question #691 : Geometry

Example Question #98 : Coordinate Geometry

All GMAT Math Resources

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