QuestionFind the line equation through points (-2,1) and (1,-2). Options: a) $y=x-1$ , b) $y=x+1$ , c) $y=-2x+1$ , d) $y=1-x$ , e) $y=-x-1$ .

Studdy Solution

STEP 1

Assumptions1. We are given two points on the line $(-,1)$ and $(1,-)$ . . We are looking for the equation of the line in the form $y=mx+c$ , where $m$ is the slope and $c$ is the y-intercept.

STEP 2

First, we need to find the slope of the line. The slope is given by the formula $m = \frac{y2 - y1}{x2 - x1}$

STEP 3

Now, plug in the given values for $x1$ , $y1$ , $x2$ , and $y2$ to calculate the slope.
$m = \frac{-2 -1}{1 - (-2)}$

STEP 4

Calculate the slope.
$m = \frac{-3}{3} = -1$

STEP 5

Now that we have the slope, we can find the y-intercept, $c$ . We can use the formula $y = mx + c$ and one of the given points to find $c$ . Let's use the point $(-2,1)$ .
$1 = -1 \cdot -2 + c$

STEP 6

olve the equation for $c$ .
$c =1 -2 = -1$

STEP 7

Now that we have both the slope and the y-intercept, we can write the equation of the line.
$y = -1x -1$ The equation of the line through the points $(-2,1)$ and $(1,-2)$ is $y = -x -1$ .

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QuestionFind the line equation through points (-2,1) and (1,-2). Options: a) $y=x-1$ , b) $y=x+1$ , c) $y=-2x+1$ , d) $y=1-x$ , e) $y=-x-1$ .

Studdy Solution

STEP 1

Assumptions1. We are given two points on the line $(-,1)$ and $(1,-)$ . . We are looking for the equation of the line in the form $y=mx+c$ , where $m$ is the slope and $c$ is the y-intercept.

STEP 2

First, we need to find the slope of the line. The slope is given by the formula $m = \frac{y2 - y1}{x2 - x1}$

STEP 3

Now, plug in the given values for $x1$ , $y1$ , $x2$ , and $y2$ to calculate the slope.
$m = \frac{-2 -1}{1 - (-2)}$

STEP 4

Calculate the slope.
$m = \frac{-3}{3} = -1$

STEP 5

Now that we have the slope, we can find the y-intercept, $c$ . We can use the formula $y = mx + c$ and one of the given points to find $c$ . Let's use the point $(-2,1)$ .
$1 = -1 \cdot -2 + c$

STEP 6

olve the equation for $c$ .
$c =1 -2 = -1$

STEP 7

Now that we have both the slope and the y-intercept, we can write the equation of the line.
$y = -1x -1$ The equation of the line through the points $(-2,1)$ and $(1,-2)$ is $y = -x -1$ .

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QuestionFind the line equation through points (-2,1) and (1,-2). Options: a) y=x−1y=x-1y=x−1, b) y=x+1y=x+1y=x+1, c) y=−2x+1y=-2x+1y=−2x+1, d) y=1−xy=1-xy=1−x, e) y=−x−1y=-x-1y=−x−1.

Studdy Solution

STEP 1

Assumptions1. We are given two points on the line (−,1)(-,1)(−,1) and (1,−)(1,-)(1,−). . We are looking for the equation of the line in the form y=mx+cy=mx+cy=mx+c, where mmm is the slope and ccc is the y-intercept.

STEP 2

First, we need to find the slope of the line. The slope is given by the formulam=y2−y1x2−x1m = \frac{y2 - y1}{x2 - x1}m=x2−x1y2−y1​

STEP 3

Now, plug in the given values for x1x1x1, y1y1y1, x2x2x2, and y2y2y2 to calculate the slope.m=−2−11−(−2)m = \frac{-2 -1}{1 - (-2)}m=1−(−2)−2−1​

STEP 4

Calculate the slope.m=−33=−1m = \frac{-3}{3} = -1m=3−3​=−1

STEP 5

Now that we have the slope, we can find the y-intercept, ccc. We can use the formula y=mx+cy = mx + cy=mx+c and one of the given points to find ccc. Let's use the point (−2,1)(-2,1)(−2,1).1=−1⋅−2+c1 = -1 \cdot -2 + c1=−1⋅−2+c

STEP 6

olve the equation for ccc.c=1−2=−1c =1 -2 = -1c=1−2=−1

STEP 7

Now that we have both the slope and the y-intercept, we can write the equation of the line.y=−1x−1y = -1x -1y=−1x−1The equation of the line through the points (−2,1)(-2,1)(−2,1) and (1,−2)(1,-2)(1,−2) is y=−x−1y = -x -1y=−x−1.

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QuestionFind the line equation through points (-2,1) and (1,-2). Options: a) $y=x-1$ , b) $y=x+1$ , c) $y=-2x+1$ , d) $y=1-x$ , e) $y=-x-1$ .

Assumptions1. We are given two points on the line $(-,1)$ and $(1,-)$ . . We are looking for the equation of the line in the form $y=mx+c$ , where $m$ is the slope and $c$ is the y-intercept.

First, we need to find the slope of the line. The slope is given by the formula $m = \frac{y2 - y1}{x2 - x1}$

Now, plug in the given values for $x1$ , $y1$ , $x2$ , and $y2$ to calculate the slope.
$m = \frac{-2 -1}{1 - (-2)}$

Calculate the slope.
$m = \frac{-3}{3} = -1$

Now that we have the slope, we can find the y-intercept, $c$ . We can use the formula $y = mx + c$ and one of the given points to find $c$ . Let's use the point $(-2,1)$ .
$1 = -1 \cdot -2 + c$

olve the equation for $c$ .
$c =1 -2 = -1$

Now that we have both the slope and the y-intercept, we can write the equation of the line.
$y = -1x -1$ The equation of the line through the points $(-2,1)$ and $(1,-2)$ is $y = -x -1$ .