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AVprozaik [17]
1 year ago
14

write the equation in slope intercept form for a line that will pass through (0,3) and have a slope of (-8,15)

Mathematics
1 answer:
egoroff_w [7]1 year ago
3 0

The equation of line with the slope m in the slope intercept form is :

y = mx + b

Slope can express as :

\text{ Slope=}\frac{y_2-y_1}{x_2-x_1}

Substitute the value :

(x_1,y_1)=(0,3),(x_2,y_2)=(-8,15)

\begin{gathered} \text{ Slope=}\frac{y_2-y_1}{x_2-x_1} \\ Sl\text{ope=}\frac{15-3}{-8-0} \\ \text{ slope=}\frac{12}{-8} \\ \text{slope}=\frac{3}{-2} \end{gathered}

Substitute the value of slope in the equation of line:

\begin{gathered} y-3=\frac{3}{-2}(x-0) \\ y-3\text{ =-}\frac{3}{2}x \\ y=-\frac{3}{2}x+3 \end{gathered}

Equation of line in slope intercept form is :

y = -3/2x + 3

Slope = -3/2

Answer : y = -3/2x + 3

Slope = -3/2

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Unit 3 parallel and perpendicular lines homework 4 parallel line proofs
Alex17521 [72]

Answer:

1) c ║ d by consecutive interior angles theorem

2) m∠3 + m∠6 = 180° by transitive property

3) ∠2 ≅ ∠5 by definition of congruency

4) t ║ v                                    {}                   Corresponding angle theorem

5) ∠14 and ∠11  are supplementary         {}  Definition of supplementary angles

6) ∠8 and ∠9  are supplementary    {}        Consecutive  interior angles theorem

Step-by-step explanation:

1) Statement                                {}                                     Reason

m∠4 + m∠7 = 180°                                 {}   Given

m∠4 ≅ m∠6                                {}              Vertically opposite angles

m∠4 = m∠6                               {}                Definition of congruency

m∠6 + m∠7 = 180°                                {}    Transitive property

m∠6 and m∠7 are supplementary     {}     Definition of supplementary angles

∴ c ║ d                               {}                       Consecutive interior angles theorem

2) Statement                                {}                                     Reason

m∠3 = m∠8                                 {}           Given

m∠8 + m∠6 = 180°                {}                 Sum of angles on a straight line

∴ m∠3 + m∠6 = 180°               {}               Transitive property

3) Statement                                {}                                     Reason

p ║ q                                 {}                    Given

∠1 ≅ ∠5                               {}                  Given

∠1 = ∠5                               {}                   Definition of congruency

∠2 ≅ ∠1                               {}                  Alternate interior angles theorem

∠2 = ∠1                               {}                   Definition of congruency

∠2 = ∠5                                  {}               Transitive property

∠2 ≅ ∠5                                  {}              Definition of congruency.

4) Statement                                {}                                     Reason

∠1 ≅ ∠5                                  {}                Given

∠3 ≅ ∠4                               {}                  Given

∠1 = ∠5                               {}                   Definition of congruency

∠3 = ∠4                               {}                  Definition of congruency

∠5 ≅ ∠4                               {}                 Vertically opposite angles

∠5 = ∠4                               {}                  Definition of congruency

∠5 = ∠3                                  {}               Transitive property

∠1 = ∠3                                  {}                Transitive property

∠1 ≅ ∠3                                  {}                Definition of congruency.

t ║ v                                    {}                   Corresponding angle theorem

5) Statement                                {}                                     Reason

∠5 ≅ ∠16                                  {}              Given

∠2 ≅ ∠4                               {}                  Given

∠5 = ∠16                               {}                  Definition of congruency

∠2 = ∠4                               {}                   Definition of congruency

EF ║ GH                               {}                  Corresponding angle theorem

∠14 ≅ ∠16                               {}                Corresponding angles

∠14 = ∠16                               {}                 Definition of congruency

∠5 = ∠14                                  {}               Transitive property

∠5 + ∠11 = 180°                {}                       Sum of angles on a straight line

∠14 + ∠11 = 180°                                {}      Transitive property

∠14 and ∠11  are supplementary         {}  Definition of supplementary angles  

6) Statement                                {}                                     Reason

l ║ m                                 {}                      Given

∠4 ≅ ∠7                               {}                  Given

∠4 = ∠7                               {}                   Definition of congruency

∠2 ≅ ∠7                               {}                  Alternate angles

∠2 = ∠7                               {}                   Definition of congruency

∠2 = ∠4                                  {}               Transitive property

∠2 ≅ ∠4                               {}                  Definition of congruency

∠2 and ∠4 are corresponding angles   {} Definition

DA ║ EB                               {}                  Corresponding angle theorem

∠8 and ∠9  are consecutive  interior angles    {} Definition

∠8 and ∠9  are supplementary    {}        Consecutive  interior angles theorem.

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