Question Find the y-intercept of the line passing through the points $(8,6)$ and $(4,22)$ .

Studdy Solution

STEP 1

Assumptions
1. The line passes through the points $(8,6)$ and $(4,22)$ .
2. The $y$ -intercept is the point where the line crosses the $y$ -axis, which means its $x$ -coordinate is $0$ .

STEP 2

First, we need to find the slope of the line using the two given points. The slope ( $m$ ) is calculated using the formula:
$m = \frac{y_2 - y_1}{x_2 - x_1}$

STEP 3

Plug in the coordinates of the given points into the slope formula.
$m = \frac{22 - 6}{4 - 8}$

STEP 4

Calculate the slope.
$m = \frac{16}{-4} = -4$

STEP 5

Now that we have the slope, we can use the point-slope form of the equation of a line to find the equation. The point-slope form is:
$y - y_1 = m(x - x_1)$

STEP 6

Choose one of the points to use in the point-slope form. We will use the point $(8,6)$ .
$y - 6 = -4(x - 8)$

STEP 7

Distribute the slope $-4$ into the parentheses.
$y - 6 = -4x + 32$

STEP 8

Add $6$ to both sides of the equation to solve for $y$ .
$y = -4x + 38$

STEP 9

Now that we have the equation of the line in slope-intercept form, we can find the $y$ -intercept by setting $x = 0$ .
$y = -4(0) + 38$

STEP 10

Calculate the $y$ -intercept.
$y = 38$
The $y$ -intercept of the line is $38$ .

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Question Find the y-intercept of the line passing through the points $(8,6)$ and $(4,22)$ .

Studdy Solution

STEP 1

Assumptions
1. The line passes through the points $(8,6)$ and $(4,22)$ .
2. The $y$ -intercept is the point where the line crosses the $y$ -axis, which means its $x$ -coordinate is $0$ .

STEP 2

First, we need to find the slope of the line using the two given points. The slope ( $m$ ) is calculated using the formula:
$m = \frac{y_2 - y_1}{x_2 - x_1}$

STEP 3

Plug in the coordinates of the given points into the slope formula.
$m = \frac{22 - 6}{4 - 8}$

STEP 4

Calculate the slope.
$m = \frac{16}{-4} = -4$

STEP 5

Now that we have the slope, we can use the point-slope form of the equation of a line to find the equation. The point-slope form is:
$y - y_1 = m(x - x_1)$

STEP 6

Choose one of the points to use in the point-slope form. We will use the point $(8,6)$ .
$y - 6 = -4(x - 8)$

STEP 7

Distribute the slope $-4$ into the parentheses.
$y - 6 = -4x + 32$

STEP 8

Add $6$ to both sides of the equation to solve for $y$ .
$y = -4x + 38$

STEP 9

Now that we have the equation of the line in slope-intercept form, we can find the $y$ -intercept by setting $x = 0$ .
$y = -4(0) + 38$

STEP 10

Calculate the $y$ -intercept.
$y = 38$
The $y$ -intercept of the line is $38$ .

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Question Find the y-intercept of the line passing through the points (8,6)(8,6)(8,6) and (4,22)(4,22)(4,22).

Studdy Solution

STEP 1

Assumptions1. The line passes through the points (8,6)(8,6)(8,6) and (4,22)(4,22)(4,22).2. The yyy-intercept is the point where the line crosses the yyy-axis, which means its xxx-coordinate is 000.

STEP 2

First, we need to find the slope of the line using the two given points. The slope (mmm) is calculated using the formula:m=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1}m=x2​−x1​y2​−y1​​

STEP 3

Plug in the coordinates of the given points into the slope formula.m=22−64−8m = \frac{22 - 6}{4 - 8}m=4−822−6​

STEP 4

Calculate the slope.m=16−4=−4m = \frac{16}{-4} = -4m=−416​=−4

STEP 5

Now that we have the slope, we can use the point-slope form of the equation of a line to find the equation. The point-slope form is:y−y1=m(x−x1)y - y_1 = m(x - x_1)y−y1​=m(x−x1​)

STEP 6

Choose one of the points to use in the point-slope form. We will use the point (8,6)(8,6)(8,6).y−6=−4(x−8)y - 6 = -4(x - 8)y−6=−4(x−8)

STEP 7

Distribute the slope −4-4−4 into the parentheses.y−6=−4x+32y - 6 = -4x + 32y−6=−4x+32

STEP 8

Add 666 to both sides of the equation to solve for yyy.y=−4x+38y = -4x + 38y=−4x+38

STEP 9

Now that we have the equation of the line in slope-intercept form, we can find the yyy-intercept by setting x=0x = 0x=0.y=−4(0)+38y = -4(0) + 38y=−4(0)+38

STEP 10

Calculate the yyy-intercept.y=38y = 38y=38The yyy-intercept of the line is 383838.

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Question Find the y-intercept of the line passing through the points $(8,6)$ and $(4,22)$ .

Assumptions
1. The line passes through the points $(8,6)$ and $(4,22)$ .
2. The $y$ -intercept is the point where the line crosses the $y$ -axis, which means its $x$ -coordinate is $0$ .

First, we need to find the slope of the line using the two given points. The slope ( $m$ ) is calculated using the formula:
$m = \frac{y_2 - y_1}{x_2 - x_1}$

Plug in the coordinates of the given points into the slope formula.
$m = \frac{22 - 6}{4 - 8}$

Calculate the slope.
$m = \frac{16}{-4} = -4$

Now that we have the slope, we can use the point-slope form of the equation of a line to find the equation. The point-slope form is:
$y - y_1 = m(x - x_1)$

Choose one of the points to use in the point-slope form. We will use the point $(8,6)$ .
$y - 6 = -4(x - 8)$

Distribute the slope $-4$ into the parentheses.
$y - 6 = -4x + 32$

Add $6$ to both sides of the equation to solve for $y$ .
$y = -4x + 38$

Now that we have the equation of the line in slope-intercept form, we can find the $y$ -intercept by setting $x = 0$ .
$y = -4(0) + 38$

Calculate the $y$ -intercept.
$y = 38$
The $y$ -intercept of the line is $38$ .