ISEE Lower Level Quantitative Reasoning - How to find a line on a coordinate plane

Vt_custom_xy_xylinesegment1

Which equation of a line is parallel to line segment $\bar{AB}$ ?

$y=\frac{9}{13}-8$

$y=\frac{5}{12}+4$

$y=-\frac{9}{13}-6$

$y=\frac{13}{9}+5$

Explanation

In order for the equation to represent a line that is parallel to the line that is shown, the equation must have the same slope as line segment $\bar{AB}$ .

Since, line segment $\bar{AB}$ has a slope of $\frac{9}{13}$ , the correct equation is: $y=\frac{9}{13}-8$

Find the equation that represents a line that has a intercept of .

$y=\frac{3}{4}x-7$

$y=\frac{3}{4}x+7$

$y=\frac{3}{4}x-5$

$y=\frac{3}{4}x+5$

Explanation

To identify the correct equation, apply the formula , where represents the slope of the line and the intercept.

Thus, the line that passes through the axis at is $y=\frac{3}{4}x-7$

Vt_custom_xy_xysegment_3

At what coordinate point does the line intersect with the line segment shown above?

Explanation

Since, is perpendicular to the points must cross at , because it is the only coordinate point that both lines pass through.

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Find coordinates for the midpoint of the line segment above.

Explanation

To find the midpoint of this line segment, you could apply the midpoint formula. However, most students preparing for this exam will not learn the midpoint formula for several years. Therefore, the most effective way to find the midpoint is to find the difference between the two end points' values, and then divide the difference in half to find the middle coordinate.

Since, the difference between and is .

$\frac{17}{2}=8.5$ .

Thus, the midpoint is increments away from each of the points. By counting increments from either point, you'll land on the midpoint coordinate of .

Vt_custom_xy_xysegment_3

The points in the above line segment are apart of which of the following linear equations?

Explanation

The above line segment is a horizontal line that passes through the axis at Since this line is horizontal, it does not have a slope. Therefore, is the correct answer.

Vt_custom_xy_xylinesegment1

Line segment $\bar{AB}$ has endpoints and . What is the slope of the line segment?

$\frac{9}{13}$

$\frac{13}{9}$

$-\frac{9}{13}$

$\frac{1}{3}$

Explanation

To find the slope of the line that passes through these two coordinate points, apply the formula:

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

Thus the correct answer is:
$\frac{6--3}{7--6}=\frac{6+3}{7+6}=\frac{9}{13}$

Vt_custom_xy_xysegment_3

Find the length of the line segment above.

Explanation

To find the length of this line segment find the difference between each of the two end points values, since they have the same value.

The difference between and is .

Vt_custom_xy_xyline5

At which coordinate point does this line segment cross the -axis?

Explanation

Keep in mind that the values in the coordinate points are , thus the point is the point at which the line segment passes through the axis.

Find the slope of the line that passes through the coordinate points and .

$\frac{1}{2}$

$-\frac{1}{2}$

Explanation

To find the slope of the line that passes through these two coordinate points, apply the formula:

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

Thus the correct answer is:

$\frac{ -1-4}{2--3}=\frac{-5}{5}=-\frac{5}{5}=-1$

Find the equation of a line that has the steepest slope?

$y=\frac{4}{5}x-5$

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

$y=\frac{3}{5}x+7$

$y=\frac{2}{5}x-5$

Explanation

To find which equation of a line has the steepest slope, apply the formula: , where represents the slope of the line and represents the intercept.

Also, note that $m=\frac{rise}{run}$ , meaning the change in the value, over the change in the value. The greater the absolute value m value of an equation is the steeper the slope of the line is.