If you're given coordinates of 2 points, how do you find the y-intercept?

Question

If you're given coordinates of 2 points, how do you find the y-intercept?

1 Answer

Impact of this question

119201 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-07-22T11:44:19

The y-intercept is $1$ $1$

Explanation:

Step 1.
Find the slope using the equation $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ $m=(y_2-y_1)/(x_2-x_1)$ , where $m$ $m$ is the slope, and $(x_{1}, y_{1})$ $(x_1,y_1)$ and $(x_{2}, y_{2})$ $(x_2,y_2)$ are the two points on the line.

Example
Find the slope of a line passing through the points $(- 2, - 1)$ $(color(red)(-2),color(blue)(-1))$ and $(4, 3)$ $(color(red)(4),color(blue)(3))$ .

$(- 2, - 1) = (x_{1}, y_{1})$ $(color(red)(-2),color(blue)(-1))=(color(red)(x_1), color(blue)(y_1))$

$(4, 3) = (x_{2}, y_{2})$ $(color(red)(4),color(blue)(3))=(color(red)(x_2),color(blue)(y_2))$

$m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}} = \frac{3 - (- 1)}{4 - (- 2)}$ $color(purple)m=(color(blue)(y_2)-color(blue)(y_1))/(color(red)(x_2)-color(red)(x_1))=(color(blue)(3)-(color(blue)(-1)))/(color(red)(4)-(color(red)(-2))$ = $\frac{4}{6} = \frac{2}{3}$ $color(blue)(4)/color(red)6=color(purple)(2)/color(purple)3$

Step 2.

Determine the point-slope form of a linear equation $(y - y_{1}) = m (x - x_{1})$ $(y-y_1)=m(x-x_1)$ , where $(x_{1}, y_{1})$ $(x_1,y_1)$ is one of the points.

Continue with the previous example.

$(y - (- 1)) = \frac{2}{3} (x - (- 2))$ $(color(blue)(y)-(color(blue)(-1)))=color(purple)(2/3)(color(red)(x)-(color(red)(-2)))$ =

$y + 1 = \frac{2}{3} (x + 2)$ $color(blue)(y)+color(blue)(1)=color(purple)(2/3)(color (red)(x)+color(red)(2))$

Convert to slope-intercept form $y = m x + b$ $y=mx+b$ , where $m$ $m$ is the slope and $b$ $b$ is the y-intercept, by solving for $y$ $y$ .

$y + 1 = \frac{2}{3} x + 2$ $y+1=2/3x+2$

Subtract $1$ $1$ from both sides.

$y = \frac{2}{3} x + 2 - 1$ $y=2/3x+2-1$ =

$y = \frac{2}{3} x + 1$ $y=2/3x+1$

The slope intercept is $1$ $1$ .

Science

Math

Humanities

... and beyond

If you're given coordinates of 2 points, how do you find the y-intercept?

1 Answer

Explanation:

Related questions

Impact of this question