Respuesta :
Answer:
y = [tex]\frac{7}{6}[/tex] x - 3
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (9, 2 ) and (x₂, y₂ ) = (3, - 5 )
m = [tex]\frac{-5-2}{3-9}[/tex] = [tex]\frac{-7}{-6}[/tex] = [tex]\frac{7}{6}[/tex]
• Parallel lines have equal slopes , so
m = [tex]\frac{7}{6}[/tex] is the slope of the parallel line
the line crosses the y- axis at (0, - 3 ) ⇒ c = - 3
y = [tex]\frac{7}{6}[/tex] x - 3 ← equation of parallel line
Hey there!
[tex] \\ [/tex]
- Answer:
[tex] \green{\boxed{\red{\bold{\sf{y = \dfrac{7}{6}x - 3}}}}}[/tex]
[tex] \\ [/tex]
- Explanation:
To find the equation of a line, we first have to determine its slope knowing that parallel lines have the same slope.
Let the line that we are trying to determine its equation be [tex] \: \sf{d_1} \: [/tex] and the line that is parallel to [tex] \: \sf{d_1} \: [/tex] be [tex] \: \sf{d_2} \: [/tex] .
[tex] \sf{d_2} \:[/tex] passes through the points (9 , 2) and (3 , -5) which means that we can find its slope using the slope formula:
[tex] \sf{m = \dfrac{\Delta y}{\Delta x} = \dfrac{\green{y_2} - \orange{y_1}}{\red{x_2} - \blue{x_1 }}} [/tex]
[tex] \\ [/tex]
⇒Subtitute the values :
[tex] \sf{(\overbrace{\blue{9}}^{\blue{x_1}}\: , \: \overbrace{\orange{2}}^{\orange{y_1}}) \: \: and \: \: (\overbrace{\red{3}}^{\red{x_2}} \: , \: \overbrace{\green{-5}}^{\green{y_2}} )} [/tex]
[tex] \implies \sf{m = \dfrac{\Delta y}{\Delta x} = \dfrac{\green{-5} - \orange{2}}{\red{ \: \: 3} - \blue{9 }} = \dfrac{ - 7}{ - 6} = \boxed{ \bold{\dfrac{7}{6} }}}[/tex]
[tex] \sf{\bold{The \: slope \: of \: both \: lines \: is \: \dfrac{7}{6}}} [/tex].
Assuming that we want to get the equation in Slope-Intercept Form, let's substitute m = 7/6:
Slope-Intercept Form:
[tex] \sf{y = mx + b} \\ \sf{Where \: m \: is \: the \: slope \: of \: the \: line \: and \: b \: is \: the \: y-intercept.} [/tex]
[tex] \implies \sf{y = \bold{\dfrac{7}{6}}x + b} [/tex] [tex] \\ [/tex]
We know that the coordinates of the point (0 , -3) verify the equation since it is on the line [tex] \: \sf{d_1} \: [/tex]. Now, replace y with -3 and x with 0:
[tex] \implies \sf{\overbrace{-3}^{y} = \dfrac{7}{8} \times \overbrace{0}^{x} + b} \\ \\ \implies \sf{-3 = 0 + b} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \implies \sf{\boxed{\bold{b = -3}} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]
Therefore, the equation of the line [tex] \: \bold{d_1} \: [/tex] is [tex] \green{\boxed{\red{\bold{\sf{y = \dfrac{7}{6}x - 3}}}}} [/tex]
[tex] \\ [/tex]
▪️Learn more about finding the equation of a line that is parallel to another one here:
↣https://brainly.com/question/27497166
