Intercepts and Curves - Math

Card 0 of 632

Question

True or false: The lines of the equations

and

have the same -intercept.

Answer

The -intercept of a line is the point at which it intersects the -axis; its -coordinate at this point is 0, so its -coordinate can be found by substituting 0 for in the equation and solving for . Do this with both equations:

$2 \cdot 0 +y = 12$

The -intercept of the line is at .

$\frac{2y }{2}$= $\frac{12}{2}$

The -intercept of the line is at .

The two lines have different -intercepts.

Compare your answer with the correct one above

Question

True or false: the lines of the equations

and

have the same -intercept.

Answer

The -intercept of a line is the point at which it intersects the -axis; its -coordinate at this point is 0.

The -coordinate of the line of the equation

can be found by substituting 0 for in the equation and solving for :

The -intercept of this line is at .

The line with equation is a horizontal line with its -intercept at , so the -intercept line of the equation has its -intercept at as well.

Both lines indeed have the same -intercept.

Compare your answer with the correct one above

Question

What is the x-intercept for the line ?

Answer

To find the x-intercept, plug in for , since the x-axis is where .

add to both sides

divide both sides by

Compare your answer with the correct one above

Question

If a line's -intercept is . and the -intercept is , what is the equation of the line?

Answer

Write the equation in slope-intercept form:

We were given the -intercept, , which means :

Given the -intercept is , the point existing on the line is . Substitute this point into the slope-intercept equation and then solve for to find the slope:

Add to each side of the equation:

Divide each side of the equation by :

$m=\frac{1}{5}$$

Substituting the value of back into the slope-intercept equation, we get:

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

By subtracting $-$\frac{1}{5}$x$ on both sides, we can rearrange the equation to put it into standard form:

$-$\frac{1}{5}$x+y=-1$

Compare your answer with the correct one above

Question

Find the -intercept of:

Answer

To find the x-intercept, we need to find the value of when .

So we first set to zero.

turns into

Lets subtract from both sides to move to one side of the equation.

After doing the arithmetic, we have

.

Divide by from both sides

$\frac{-4x}{-4}$=\frac{2}{-4}$

Compare your answer with the correct one above

Question

What is the -intercept of:

Answer

To find the y-intercept, we set

So

turns into

.

After doing the arithmetic we get

.

Compare your answer with the correct one above

Question

Find the y-intercept of the line $-14x+\frac{1}{4}$y=2$ .

Answer

Recall that at the y-intercept, the line crosses the y-axis. This means that at the y-intercept, the value of the x-coordinate is .

Plug in for into the equation to find the y-intercept.

$-14x+\frac{1}{4}$y=2$

$-14(0)+\frac{1}{4}$y=2$

$$\frac{1}{4}$y=2$

The y-intercept for this line is .

Compare your answer with the correct one above

Question

What is the -intercept of:

Answer

The x-intercept can be found where

So

turns into

.

Lets subtract from both sides to solve for .

After doing the arithmetic we have

.

Divide both sides by

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

Compare your answer with the correct one above

Question

Suppose two intercepts create a line. If the -intercept is and -intercept is , what is the equation of the line?

Answer

Rewrite the intercepts in terms of points.

X-intercept of 1: .

Y-intercept of 2:

Write the slope-intercept form for linear equations.

Substititute the y-intercept into the slope-intercept equation.

Substitute both the x-intercept point and the y-intercept into the equation to solve for slope.

Rewrite by substituting the values of and into the y-intercept form.

Compare your answer with the correct one above

Question

Which equation has a y-intercept at 2 and x-intercepts at -1 and 6?

Answer

In order for the equation to have x-intercepts at -1 and 6, it must have $\small (x+1)$ and as factors. This leaves us with only 2 choices, $\small \small y = (x+1)(x-6)$ or $\small y = $\frac{-1}{3}$(x+1)(x-6)$

This equation must also have a y-intercept of 2. This means that plugging in 0 for x will gives us a y-value of 2. Because we have two options, we could plug in 0 for x in each to see which gives us an answer of 2:

a) $\small y = (0+1)(0-6) = 1-6 = -6$ we can eliminate that choice

b) $\small y= -$\frac{1}{3}$(0+1)(0-6) = -$\frac{1}{3}$1*-6 = 2$ this must be the right choice.

If we hadn't been given multiple options, we could have set up the following equation to figure out the third factor:

$\small 2 = C(0+1)(0-6)$

$\small 2 = C1-6$

$\small 2 = -6C$ divide by -6

$\small -$\frac{1}{3}$ = C$

Compare your answer with the correct one above

Question

Which equation would have an x-intercept at $\small x=2$ and a y-intercept at $\small y=-3$ ?

Answer

We're writing the equation for a line passing through the points $\small (0,-3)$ and $\small (2,0)$ . Since we already know the y-intercept, we can figure out the slope of this line and then write a slope-intercept equation.

To determine the slope, divide the change in y by the change in x:

$\small $\frac{-3 - 0 }{ 0 - 2 }$ = $\frac{-3}{-2}$ = $\frac{3}$2$

The equation for this line would be $\small y = $\frac{3}{2}$x - 3$ .

Compare your answer with the correct one above

Question

Write the equation of a line with intercepts and

Answer

The line will eventually be in the form where is the y-intercept.

The y-intercept in this case is .

To find the equation, plug in for , and the other point, as x and y:

add to both sides

This means the equation is

Compare your answer with the correct one above

Question

Which equation has the x- and y-intercepts and ?

Answer

Since this line has the y-intercept , we know that in the form ,

We can plug in the other intercept's coordinates for and to solve for :

subtract

divide by

$$\frac{-7}{2}$ = m$

The line is $y = -$\frac{7}{2}$x + 7$

Compare your answer with the correct one above

Question

What are the and -intercepts of the line defined by the equation:

Answer

To find the intercepts of a line, we must set the and values equal to zero and then solve.

Compare your answer with the correct one above

Question

Given the line what is the sum of the and intercepts?

Answer

The intercepts cross an axis.

For the intercept, set to get

For the intercept, set to get

So the sum of the intercepts is .

Compare your answer with the correct one above

Question

Find the y-intercept of the line $2x+\frac{2}{3}$y=6$ .

Answer

Recall that at the y-intercept, the line crosses the y-axis. This means that at the y-intercept, the value of the x-coordinate is .

Plug in for into the equation to find the y-intercept.

$2x+\frac{2}{3}$y=6$

$2(0)+\frac{2}{3}$y=6$

$$\frac{2}{3}$y=6$

The y-intercept for this line is .

Compare your answer with the correct one above

Question

What is the -intercept of the following line:

Answer

The -intercept is the point where the y-value is equal to 0. Therefore,

Compare your answer with the correct one above

Question

Which of the following statements regarding the x and y intercepts of the equation is true?

Answer

To find the x-intercept, we simply plug into our function. giving us . We can factor that equation, making it . We can not solve for , and we get . To find the y-intercept, we do the same thing, however this time, we plug in instead. This leaves us with . With an x-intercept of and a y-intercept of , it is clear that the y-intercept is greater than the x-intercept.

Compare your answer with the correct one above

Question

Find the -intercept of the following function.

Answer

To find the x-intercept, set y equal to 0.

Now solve for x by dividing by 3 on both sides.

$$\frac{9}{3}$=\frac{3}{3}$x$

This reduces to,

Compare your answer with the correct one above

Question

Find the -intercept of the following function.

Answer

To find the y-intercept, set x equal to 0.

Now solve for y.

Compare your answer with the correct one above

Tap the card to reveal the answer