Intercepts and Curves

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Math › Intercepts and Curves

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A straight line passes through the points and .

What is the -intercept of this line?

Explanation

First calculate the slope:

$(\text{change in Y})/(\text{change in x}) = (1-2)/(3-2) = -1$

The standard equation for a line is .

In this equation, is the slope of the line, and is the -intercept. All points on the line must fit this equation. Plug in either point (1,3) or (2,2).

Plugging in (1,3) we get .

Therefore, .

Our equation for the line is now:

To find the -intercept, we plug in :

Thus, the -intercept the point (4,0).

A straight line passes through the points and .

What is the -intercept of this line?

Explanation

First calculate the slope:

$(\text{change in Y})/(\text{change in x}) = (1-2)/(3-2) = -1$

The standard equation for a line is .

In this equation, is the slope of the line, and is the -intercept. All points on the line must fit this equation. Plug in either point (1,3) or (2,2).

Plugging in (1,3) we get .

Therefore, .

Our equation for the line is now:

To find the -intercept, we plug in :

Thus, the -intercept the point (4,0).

What is the x-intercept of ?

$-\frac{5}{3}$

$\frac{3}{5}$

$\frac{6}{5}$

$-\frac{3}{5}$

$-\frac{10}{3}$

Explanation

To find the x-intercept, set y equal to zero and solve:

Subtract from both sides:

Divide both sides by to isolate x:

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

What is the x-intercept of ?

$-\frac{5}{3}$

$\frac{3}{5}$

$\frac{6}{5}$

$-\frac{3}{5}$

$-\frac{10}{3}$

Explanation

To find the x-intercept, set y equal to zero and solve:

Subtract from both sides:

Divide both sides by to isolate x:

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

The center of a circle is and its radius is . Which of the following could be the equation of the circle?

$(x - 2)^{2} + (y - 4)^{2} = 100$

$(x + 2)^{2} + (y + 4)^{2} = 100$

$(x - 2)^{2} + (y - 4)^{2} = 10$

$x^{2} + y^{2} = 100$

$2x^{2} + 4y^{2} = 100$

Explanation

The general equation of a circle is $(x - h)^{2} + (y - k)^{2} = r^{2}$ , where the center of the circle is and the radius is .

Thus, we plug the values given into the above equation to get $(x - 2)^{2} + (y - 4)^{2} = 100$ .

The center of a circle is and its radius is . Which of the following could be the equation of the circle?

$(x - 2)^{2} + (y - 4)^{2} = 100$

$(x + 2)^{2} + (y + 4)^{2} = 100$

$(x - 2)^{2} + (y - 4)^{2} = 10$

$x^{2} + y^{2} = 100$

$2x^{2} + 4y^{2} = 100$

Explanation

The general equation of a circle is $(x - h)^{2} + (y - k)^{2} = r^{2}$ , where the center of the circle is and the radius is .

Thus, we plug the values given into the above equation to get $(x - 2)^{2} + (y - 4)^{2} = 100$ .

Find the -intercepts of

Explanation

Take out a from the original equation so that you can set the expression equal to and get your -intercepts and .

Find the -intercepts of

Explanation

Take out a from the original equation so that you can set the expression equal to and get your -intercepts and .

What is the x-intercept of $y=\frac{2}{3}x+6$ ?

Explanation

To solve for the x-intercept, we set the value equal to and solve.

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

$0=\frac{2}{3}x+6$

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

$\frac{3}{2}*-6=x$

Find the x and y-intercepts of the following equation:

y-intercept:

x-intercept: $(\frac{13}{6},0)$

y-intercept:

x-intercept: $(\frac{13}{6},0)$

y-intercept:

x-intercept: $(-\frac{13}{6},0)$

y-intercept:

x-intercept: $(-\frac{13}{6},0)$

y-intercept: $(\frac{13}{6},0)$

x-intercept:

Explanation

To find the y-intercept, substitute zero for x and solve for y:

The y-intercept is at point .

To find the x-intercept, substitute zero for y and solve for x:

$x=\frac{13}{6}$

The x-intercept is at point $(\frac{13}{6},0)$ .

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