QuestionDetermine the line equation through points $(-3,-1)$ and $(2,4)$ .

Studdy Solution

STEP 1

Assumptions1. We have two points, $(-3,-1)$ and $(,4)$ , through which the line passes. . We are looking for the equation of the line in the form $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept.

STEP 2

First, we need to find the slope of the line. The slope ( $m$ ) 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.
$m = \frac{ - (-1)}{2 - (-3)}$

STEP 4

Calculate the slope.
$m = \frac{4 +1}{2 +3} = \frac{}{} =1$

STEP 5

Now that we have the slope, we can find the y-intercept ( $b$ ) using the formula $b = y - mx$ We can use either of the given points for $x$ and $y$ in this formula. Let's use the point $(-3,-1)$ .

STEP 6

Plug in the values for $x$ , $y$ , and $m$ to calculate $b$ .
$b = -1 -1(-3)$

STEP 7

Calculate the y-intercept.
$b = -1 +3 =2$

STEP 8

Now that we have the slope and the y-intercept, we can write the equation of the line.
$y = mx + b$

STEP 9

Plug in the values for $m$ and $b$ to write the equation of the line.
$y =x +2$

STEP 10

implify the equation of the line.
$y = x +2$ The equation of the line that passes through the points $(-3,-)$ and $(2,4)$ is $y = x +2$ .

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