Adjon meg egy egyenletet vagy feladatot

A kamera bemenete nem felismerhető!

Megoldás - Properties of a line from two points

Slope:

m = 23

m=23

Equation of the line in slope-intercept form:

y = 23 x + 1060

y=23x+1060

x-intercept:

(- \frac{1060}{23}, 0)

(-\frac{1060}{23},0)

y-intercept:

(0, 1060)

(0,1060)

Lépések megtekintése Learn more with Tiger Try this:

Lépésről lépésre magyarázat

1. Find the slope

The slope of a line between two points equals the change in the points' y-coordinates (rise) over the change in their x-coordinates (run).

The coordinates of point 1 are: $x_{1} = - 50$ , $y_{1} = - 90$
The coordinates of point 2 are: $x_{2} = - 48$ , $y_{2} = - 44$

To find the slope, plug the points' x and y-coordinates into the formula and combine to simplify:

3 additional steps

$m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$

$m = \frac{- 44 - - 90}{- 48 - - 50}$

$m = \frac{- 44 + 90}{- 48 + 50}$

$m = \frac{46}{2}$

$m = 23$

2. Find the line equation in slope intercept form

In slope-intercept form, $y = m x + b$ , $m$ represents the slope, $b$ represents the y-intercept, and $x$ and $y$ represent the x and y-coordinates of a point on the line.
To find $b$ , plug the slope ( $m$ ) and the coordinates of a point on the line ( $x_{1}$ , $y_{1}$ ) into the slope-intercept formula:

$y = m x + b$
$m = 23$
$y_{1} = - 90$
$x_{1} = - 50$

5 additional steps

$- 90 = 23 \cdot - 50 + b$

Egyszerűsítsd a kifejezést:

$- 90 = - 1150 + b$

Cseréld fel az oldalakat:

$- 1150 + b = - 90$

Add to both sides:

$(- 1150 + b) + 1150 = - 90 + 1150$

Csoportosítsd az azonos tagokat:

$b + (- 1150 + 1150) = - 90 + 1150$

Egyszerűsítsd a számtani műveletet:

$b = - 90 + 1150$

Egyszerűsítsd a számtani műveletet:

$b = 1060$

To find the equation of the line, plug $m$ and $b$ into the slope-intercept formula:

$y = m x + b$
$m = 23$
$b = 1060$
$y = 23 x + 1060$

3. Find the x and y-intercepts

To find the x-intercept, plug 0 in for $y$ in the equation, $y = m x + b$ , and solve for $x$ :

5 additional steps

$0 = 23 x + 1060$

Swap sides:

$23 x + 1060 = 0$

Subtract from both sides:

$(23 x + 1060) - 1060 = 0 - 1060$

Egyszerűsítsd a számtani műveletet:

$23 x = 0 - 1060$

Egyszerűsítsd a számtani műveletet:

$23 x = - 1060$

Divide both sides by :

$\frac{(23 x)}{23} = \frac{- 1060}{23}$

Egyszerűsítsd a törtet:

$x = \frac{- 1060}{23}$

x-intercept: $(- \frac{1060}{23}, 0)$

To find the y-intercept, plug 0 in for $x$ in the equation, $y = m x + b$ , and solve for $y$ :

$y = 0 + 1060$

Egyszerűsítsd a számtani műveletet:

$y = 1060$

y-intercept: $(0, 1060)$

The $b$ in the slope-intercept equation, $y = m x + b$ , is always equal to the y-coordinate of the y-intercept point. In other words, if $x = 0$ then $y = b$ .

4. Graph the line

Hasznos volt ez a magyarázat?

Igen Nem

How did we do?

Kérjük, küldjön nekünk visszajelzést.

Miért érdemes ezt megtanulni

Learn more with Tiger

Whether they are horizontal, vertical, diagonal, parallel, perpendicular, intersecting, or tangent lines, it is a fact of life that straight lines are everywhere. Chances are, you know what a line is, but it is also important to understand their formal definition in order to better understand the various problems that involve them. A line is a one-dimensional figure, with a length but no width, that connects two points. After points, lines are the second smallest building blocks of shapes, which are essential for understanding our world and the spaces we find ourselves in. Additionally, understanding the slope, direction, and behavior of different types of lines is necessary for graphing and understanding certain types of information, an important skill across many industries.

Fogalmak és témák

Properties of a straight lines

Megoldás - Properties of a line from two points

Lépésről lépésre magyarázat

1. Find the slope

2. Find the line equation in slope intercept form

3. Find the x and y-intercepts

4. Graph the line

Miért érdemes ezt megtanulni

Fogalmak és témák

Kapcsolódó linkek

Legutóbb megoldott kapcsolódó feladatok