QuestionWrite the equation of the line in fully simplified slope-intercept form.

Studdy Solution

STEP 1

1. The slope-intercept form of a line is given by $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept.
2. We have two points on the line: $(-10, 11)$ and $(10, 1)$ .
3. The line equation needs to be fully simplified.

STEP 2

1. Calculate the slope $m$ of the line using the two points.
2. Use the slope and one of the points to solve for the y-intercept $b$ .
3. Write the equation in slope-intercept form and simplify if necessary.

STEP 3

Calculate the slope $m$ using the formula:
$m = \frac{y_2 - y_1}{x_2 - x_1}$
Substitute the given points $(-10, 11)$ and $(10, 1)$ :
$m = \frac{1 - 11}{10 - (-10)}$

STEP 4

Simplify the expression for the slope:
$m = \frac{-10}{20} = -\frac{1}{2}$

STEP 5

Use the slope $m = -\frac{1}{2}$ and one of the points, say $(-10, 11)$ , to find the y-intercept $b$ .
Substitute into the slope-intercept form equation $y = mx + b$ :
$11 = -\frac{1}{2}(-10) + b$

STEP 6

Solve for $b$ :
$11 = 5 + b$
$b = 11 - 5$
$b = 6$

STEP 7

Write the equation of the line in slope-intercept form using $m = -\frac{1}{2}$ and $b = 6$ :
$y = -\frac{1}{2}x + 6$
The equation of the line in fully simplified slope-intercept form is:
$\boxed{y = -\frac{1}{2}x + 6}$

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