Points and Lines - GED Math

The -intercept, the point at which a line intersects the -axis, has -coordinate 0, so substitute 0 for and solve for to find the -coordinate:

The -intercept is the point

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

The elimination method will work here. Multiply the second equation by 3 on both sides, then add to the first:

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

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

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:

, where is the slope

Now, recall that the slope is calculated from two points using the formula:

For our data, this is:

Thus, for your point-slope form of the line, you get the equation:

Just simplify things now...

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:

, where is the slope

Now, recall that the slope is calculated from two points using the formula:

For our data, this is:

Now, that is an awkward slope, but just be careful with the simplification. For the point-slope form of the line, you get the equation:

Just simplify things now...

Now, find a common denominator for the fractions. (It is .)

To solve for a question like this, the easiest thing to do is to plug in your and values to see what happens. If you get two numbers equal to each other when they are, in fact, unequal, you do not have a working case.

For example, consider the wrong option,

Substitute in your values, and you get:

or

Now, for your correct option, you get:

This certainly makes sense! It also means that the point is on the line in question!

Upon substitution of the answer choices, we will need to satisfy the equation, by plugging in the x and y-values of the points given.

The answer is:

The equation of a line in slope-intercept form is .

Write the formula for slope.

Substitute the points.

The y-intercept from the point means that .

The equation of the line is:

The answer is:

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.

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

The answer is:

Write the slope formula.

Substitute the points.

The answer is:

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.

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)

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.

Find the y-coordinate which would would make the slope between the following points equal to 5.

To find the slope of a line, use the following formula:

Now, we know all of these values except one. Let's find it.

So, our answer is

The -intercept, the point at which a line intersects the -axis, has -coordinate 0, so substitute 0 for and solve for to find the -coordinate:

The -intercept is the point

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

The elimination method will work here. Multiply the second equation by 3 on both sides, then add to the first:

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