QuestionFind an equation for the line that passes through the points $(-1,2)$ and $(-5,4)$ . $\square$ II

Studdy Solution

STEP 1

1. We are given two points: $(-1, 2)$ and $(-5, 4)$ .
2. We need to find the equation of the line passing through these points.
3. The equation of a line can be expressed in the slope-intercept form: $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept.

STEP 2

1. Calculate the slope of the line.
2. Use the slope and one of the points to find the y-intercept.
3. Write the equation of the line.

STEP 3

Calculate the slope of the line using the formula for the slope between two points $(x_1, y_1)$ and $(x_2, y_2)$ :
$m = \frac{y_2 - y_1}{x_2 - x_1}$
Substitute the given points $(-1, 2)$ and $(-5, 4)$ into the formula:
$m = \frac{4 - 2}{-5 - (-1)} = \frac{2}{-4} = -\frac{1}{2}$

STEP 4

Use the slope $m = -\frac{1}{2}$ and one of the points, say $(-1, 2)$ , to find the y-intercept $b$ using the equation $y = mx + b$ .
Substitute $x = -1$ , $y = 2$ , and $m = -\frac{1}{2}$ into the equation:
$2 = -\frac{1}{2}(-1) + b$
Solve for $b$ :
$2 = \frac{1}{2} + b$
Subtract $\frac{1}{2}$ from both sides:
$2 - \frac{1}{2} = b$
$\frac{4}{2} - \frac{1}{2} = b$
$\frac{3}{2} = b$

STEP 5

Write the equation of the line using the slope $m = -\frac{1}{2}$ and the y-intercept $b = \frac{3}{2}$ :
$y = -\frac{1}{2}x + \frac{3}{2}$
This is the equation of the line that passes through the points $(-1, 2)$ and $(-5, 4)$ .

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