Question1)) 它 $(1,1)$ and $(2,8)$ . Write its equation in slopeintercept form. 1)) Write your answer using integers, proper fractions, and improper fractions in simplest form. $\square$

Studdy Solution

STEP 1

1. We are given two points: $(1, 1)$ and $(2, 8)$ .
2. We need to find the equation of the line passing through these points in slope-intercept form, which is $y = mx + b$ .
3. The answer should use integers, proper fractions, and improper fractions in simplest form.

STEP 2

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

STEP 3

Calculate the slope of the line using the formula:
$m = \frac{y_2 - y_1}{x_2 - x_1}$
Substitute the given points $(x_1, y_1) = (1, 1)$ and $(x_2, y_2) = (2, 8)$ :
$m = \frac{8 - 1}{2 - 1} = \frac{7}{1} = 7$

STEP 4

Use the slope $m = 7$ and one of the points, say $(1, 1)$ , to find the y-intercept $b$ using the equation $y = mx + b$ .
Substitute $m = 7$ , $x = 1$ , and $y = 1$ :
$1 = 7(1) + b$
$1 = 7 + b$
Subtract 7 from both sides to solve for $b$ :
$b = 1 - 7$
$b = -6$

STEP 5

Write the equation in slope-intercept form using the slope $m = 7$ and y-intercept $b = -6$ :
$y = 7x - 6$
This is the equation of the line in slope-intercept form.

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