GED Math - Points and Lines

Find the slope given the two points: and

$-\frac{3}{2}$

$-\frac{1}{5}$

$-\frac{2}{5}$

Explanation

Write the slope formula.

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

Substitute the points.

$m = \frac{-9-(-3)}{6-2} = \frac{-6}{4} = -\frac{3}{2}$

The answer is: $-\frac{3}{2}$

What is the -coordinate of the point at which the lines of these two equations intersect?

$y = -1\frac{4}{5}$

The lines do not intersect at any point.

Explanation

The elimination method will work here. Multiply the second equation by on both sides, then add to the first:

$-2 \left (2x+y \right )= -2 \left ( 13 \right )$

$\underline{4x + 3y = 17}$

What is the -coordinate of the point at which the lines of these two equations intersect?

$y = 1 \frac{4}{5}$

$y = 7 \frac{1}{2}$

The lines of the equations do not intersect.

Explanation

The elimination method will work here. Multiply the second equation by on both sides, then add to the first:

$-2 \left (2x+y \right )= -2 \left ( 13 \right )$

$\underline{4x - 3y = 17}$

$y = -9 \div (-5) = 1 \frac{4}{5}$

Which of the following points lies on the line ?

$(2, -\frac{1}{2})$

$(-4, -\frac{7}{2})$

$(5, \frac{13}{8})$

Explanation

In order for a point to be on a line, the point must satisfy the equation. Plug in the values of and from the answer choices to see which one satisfies the equation.

Plugging in will give the following:

Since satisfies the given equation, it must be on the line.

Which of the following points is on the following line?

Explanation

Which of the following points is on the following line?

So, to test this, we can plug in each choice and solve to see if they make sense.

To save time, let's test the easier ones first. Recall that anything times 0 is 0, so we should try out the options with 0's first.

Recall that ordered pairs represent an x and a y value with the x coming first: (x,y)

So, this is not our answer. However, it does give us a hint as to the correct answer.

When we plugged in 0 for x, we got 6 on the right hand side. This means that if we plug in 0 for x, then we should get 6 for y. So, let's try out our next point.

So, our answer must be (0,6)

Which of the following points is on the line ?

$(0, \frac{3}{2})$

$(2, \frac{3}{4})$

Explanation

In order for a point to be on the line, the point must satisfy the equation given. Thus, plug in the and coordinates to see if they will give you a true equation.

If you plug in into the equation, you will get the following:

Thus, satisfies the equation and must be on the line.

What is the -coordinate of the point at which the lines of these two equations intersect?

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

$x=11\frac{1}{5}$

Explanation

The elimination method will work here. Multiply the second equation by on both sides, then add to the first:

$-3 \left (2x+y \right )= -3 \left ( 13 \right )$

$\underline{4x + 3y = 17}$

$x = -22 \div (-2)$

Given the points and , what is the equation of the line?

$y+1 = -\frac{5}{3}(x-9)$

$y= \frac{3}{2}x+14$

$y+1 = -\frac{10}{3}(x-9)$

Explanation

The equation of the line is defined in the following forms:

Point-slope form:

Standard form:

Slope intercept form:

Find the slope of the two points using the slope formula.

$m = \frac{y_2-y_1}{x_2-x_1} = \frac{9-(-1)}{3-9} = \frac{10}{-6} = -\frac{5}{3}$

Using the slope and any point or , we can substitute either into the point-slope form.

$y-(-1) = -\frac{5}{3}(x-9)$

The answer is: $y+1 = -\frac{5}{3}(x-9)$

Which of the following is an equation for the line between the points and ?

$y=\frac{12}{7}x + \frac{13}{7}$

$y=\frac{12}{7}x + \frac{62}{7}$

Explanation

Probably the easiest way to solve this question is to use the point-slope form of an equation. Remember that for that format, you need a point and the slope of the line. (Pretty obvious, given the name!) For a point , the point-slope form is: