Graphing a point - GMAT Quantitative Reasoning

Card 0 of 5

Question

The point lies on a line with slope that passes through the point .

What is ?

Answer

We first need to find an equation of the line with a slope of that passes through the point (2, 5).

Now, plug in the point and solve for .

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Question

A line goes through points . What is ?

Answer

The slope of the line through and can be found using the slope formula:

$m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

Set $x_{1}=1,x_{2} = 4, y_{1}=4,y_{2} = 8$ :

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

We can use this slope and the slope formula; set $x_{1}=1,x_{2} = -3, y_{1}=4,y_{2} = N$ :

$\frac{y_{2}-y_{1}}{x_{2}-x_{1}} = m$

$\frac{N-4}{-3-1} = \frac{4}{3}$

$\frac{N-4}{-4} = \frac{4}{3}$

$\frac{N-4}{-4}\cdot \left ( -4\right ) = \frac{4}{3} \cdot \left ( -4\right )$

$N-4= -\frac{16}{3}$

$N-4+4= -\frac{16}{3} +4$

$N= -\frac{4}{3} = -1 \frac{1}{3}$

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Question

The point lies on a line with a slope that passes through . What is the value of ?

Answer

In order to find the value of , we first need to find the equation for the line with slope that passes through the point .

Plugging in and solving for :

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Question

The point lies on a line with a slope $m=\frac{1}{2}$ that passes through . What is the value of ?

Answer

In order to find the value of , we first need to find the equation for the line with a slope $m=\frac{1}{2}$ that passes through .

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

$y-6=\frac{1}{2}x-\frac{3}{2}$

$y=\frac{1}{2}x+\frac{9}{2}$

Plugging in and solving for :

$d=\frac{1}{2}(2)+\frac{9}{2}$

$d=\frac{11}{2}$

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Question

The point lies on a line with a slope that passes through . What is the value of ?

Answer

In order to find the value of , we first need to find the equation for the line with a slope that passes through .

Plugging in and solving for :

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