Question

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Answer 1

1) Equation in Point Slope form is $y-20=-\frac{55}{4}(x+2)$

2) So, linear equation of line with slope of -1/2 and point (3,5) is $y=-\frac{1}{2}x-6\frac{1}{2}$

3) a) Slope = -1/2 and point is (4,3)

b) Slope intercept form is $y=-\frac{1}{2}x+7$

c) Standard form is: $\frac{1}{2}x+y=7$

d) x-intercept is (14,0) and y-intercept is (0,7)

Step-by-step explanation:

1) Write an equation in point slope form to model the table.

The standard form of point slope form is:

$y-y_{1} = m(x-x_{1})$

Finding Slope m:

Slope can be find using:

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

where $y_{2}=132,y_{1}=20,x_{2}=-10,x_{1}=-2$

Putting values:

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\m=\frac{132-20}{-10-(-2)}\\m=\frac{132-20}{-10+2}\\m=\frac{110}{-8}\\m=-\frac{55}{4}$

So, slope is -55/4 and considering x₁= -2 y₁=20

Putting values in point-slope form:

$y-y_{1} = m(x-x_{1})\\y-20=-\frac{55}{4}(x-(-2))\\y-20=-\frac{55}{4}(x+2)$

So, Equation in Point Slope form is $y-20=-\frac{55}{4}(x+2)$

2) Write a linear equation for the line having Slope = -1/2 and point (3,5)

We will use Point Slope form:

$y-y_{1} = m(x-x_{1})$

Putting values:

$y-5=-\frac{1}{2}(x-3)\\y-5=-\frac{1}{2}x-\frac{3}{2}\\y=-\frac{1}{2}x-\frac{3}{2}+5\\y=-\frac{1}{2}x-\frac{3+5*2}{2}\\y=-\frac{1}{2}x-\frac{13}{2}\\y=-\frac{1}{2}x-6\frac{1}{2}$

So, linear equation of line with slope of -1/2 and point (3,5) is $y=-\frac{1}{2}x-6\frac{1}{2}$

3) $y-3=-\frac{1}{2}(x-4)$

a) identify the slope and point

The standard form of point slope form is:

$y-y_{1} = m(x-x_{1})$

So, Slope = -1/2 and point is (4,3)

b) Convert to slope intercept form

The slope-intercept form is:

$y=mx+b$

Solving:

$y-3=-\frac{1}{2}(x-4)\\y-3=-\frac{1}{2}x-\frac{1}{2}*-4\\y-3=-\frac{1}{2}x+2\\y=-\frac{1}{2}x+2+5\\y=-\frac{1}{2}x+7$

So, Slope intercept form is $y=-\frac{1}{2}x+7$

c) Convert to standard form:

Standard form is : ax+by=c

Solving:

$y-3=-\frac{1}{2}(x-4)$ can be written as $y=-\frac{1}{2}x+7$

$y=-\frac{1}{2}x+7\\\frac{1}{2}x+y=7$

So, Standard form is: $\frac{1}{2}x+y=7$

d) Find the intercepts

y-y_{1} = m(x-x_{1})

• For x-intercept set y=0

$y-3=-\frac{1}{2}(x-4)$ can be written as $y=-\frac{1}{2}x+7$

$y=-\frac{1}{2}x+7\\0=-\frac{1}{2}x+7\\\frac{1}{2}x=7\\x=7*2\\x=14$

x-intercept is (14,0)

• For y-intercept set x=0

$y=-\frac{1}{2}x+7\\y=-\frac{1}{2}(0)+7\\y=7$

y-intercept is (0,7)

So, x-intercept is (14,0) and y-intercept is (0,7)

Keywords: Point Slope Form

Learn more about Point Slope Form at:

• brainly.com/question/12941985
• brainly.com/question/6431715
• brainly.com/question/9801816

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