QuestionFind the $y$ -intercept of the line with point $(2,-6)$ and slope $-\frac{3}{2}$ .

Studdy Solution

STEP 1

Assumptions1. We have a point on the line which is $(,-6)$ . The slope of the line is $-\frac{3}{}$
3. We are asked to find the y-intercept of the line, which is the point where the line crosses the y-axis (i.e., when $x=0$ )

STEP 2

The equation of a line in slope-intercept form is given by $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept. We can use this equation to find the y-intercept.

STEP 3

Substitute the given point $(2,-6)$ and the slope $-\frac{3}{2}$ into the equation of the line.
$-6 = -\frac{3}{2} \cdot2 + b$

STEP 4

implify the right side of the equation.
$-6 = -3 + b$

STEP 5

olve the equation for $b$ to find the y-intercept.
$b = - +3$

STEP 6

Calculate the value of $b$ .
$b = -3$ The y-intercept of the line is $-3$ .

Was this helpful?

QuestionFind the $y$ -intercept of the line with point $(2,-6)$ and slope $-\frac{3}{2}$ .

Studdy Solution

STEP 1

Assumptions1. We have a point on the line which is $(,-6)$ . The slope of the line is $-\frac{3}{}$
3. We are asked to find the y-intercept of the line, which is the point where the line crosses the y-axis (i.e., when $x=0$ )

STEP 2

The equation of a line in slope-intercept form is given by $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept. We can use this equation to find the y-intercept.

STEP 3

Substitute the given point $(2,-6)$ and the slope $-\frac{3}{2}$ into the equation of the line.
$-6 = -\frac{3}{2} \cdot2 + b$

STEP 4

implify the right side of the equation.
$-6 = -3 + b$

STEP 5

olve the equation for $b$ to find the y-intercept.
$b = - +3$

STEP 6

Calculate the value of $b$ .
$b = -3$ The y-intercept of the line is $-3$ .

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionFind the yyy-intercept of the line with point (2,−6)(2,-6)(2,−6) and slope −32-\frac{3}{2}−23​.

Studdy Solution

STEP 1

Assumptions1. We have a point on the line which is (,−6)(,-6)(,−6). The slope of the line is −3-\frac{3}{}−3​3. We are asked to find the y-intercept of the line, which is the point where the line crosses the y-axis (i.e., when x=0x=0x=0)

STEP 2

The equation of a line in slope-intercept form is given by y=mx+by = mx + by=mx+b, where mmm is the slope and bbb is the y-intercept. We can use this equation to find the y-intercept.

STEP 3

Substitute the given point (2,−6)(2,-6)(2,−6) and the slope −32-\frac{3}{2}−23​ into the equation of the line.−6=−32⋅2+b-6 = -\frac{3}{2} \cdot2 + b−6=−23​⋅2+b

STEP 4

implify the right side of the equation.−6=−3+b-6 = -3 + b−6=−3+b

STEP 5

olve the equation for bbb to find the y-intercept.b=−+3b = - +3b=−+3

STEP 6

Calculate the value of bbb.b=−3b = -3b=−3The y-intercept of the line is −3-3−3.

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionFind the $y$ -intercept of the line with point $(2,-6)$ and slope $-\frac{3}{2}$ .

Assumptions1. We have a point on the line which is $(,-6)$ . The slope of the line is $-\frac{3}{}$
3. We are asked to find the y-intercept of the line, which is the point where the line crosses the y-axis (i.e., when $x=0$ )

The equation of a line in slope-intercept form is given by $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept. We can use this equation to find the y-intercept.

Substitute the given point $(2,-6)$ and the slope $-\frac{3}{2}$ into the equation of the line.
$-6 = -\frac{3}{2} \cdot2 + b$

implify the right side of the equation.
$-6 = -3 + b$

olve the equation for $b$ to find the y-intercept.
$b = - +3$

Calculate the value of $b$ .
$b = -3$ The y-intercept of the line is $-3$ .