Respuesta :

semsee45

Answer:

[tex]y=\dfrac{4}{3}x-\dfrac{10}{3}[/tex]

Step-by-step explanation:

Given information:

  • [tex]y=\dfrac{4}{3}x+11[/tex]
  • Point (1, -2)

Slope-intercept form of a linear equation:

[tex]y=mx+b[/tex]

where:

  • m is the slope.
  • b is the y-intercept.

If two lines are parallel they have the same slope.

Therefore, the slope of the line that is parallel to the given line is ⁴/₃.

To find the equation of the parallel line, substitute the slope and the given point (1, -2) into slope-intercept formula and solve for b:

[tex]\implies y=mx+b[/tex]

[tex]\implies -2=\dfrac{4}{3}(1)+b[/tex]

[tex]\implies -2=\dfrac{4}{3}+b[/tex]

[tex]\implies b=-\dfrac{10}{3}[/tex]

Therefore the slope-intercept equation of the line that passes through the given point and is parallel to the given line is:

[tex]y=\dfrac{4}{3}x-\dfrac{10}{3}[/tex]

Learn more about linear equations here:

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msm555

Answer:

Solution given:

passing point(a,b)=(1,-2)

equation of line:

y=4/3*x+11

comparing above equation with y=mx+c

we get

slope(m)=4/3

again

another line is parallel to that line so

slope of another line also be same

again

we have a formula to find the equation of the line

(y-b)=m(x-a)

substituting value

y-(-2)=4/3*(x-1)

doing criss cross multiplication

3(y+2)=4(x-1)

3y+6=4x-4

6+4=4x-3y

4x-3y=10

in slope intercept form

4x-10=3y

3y=4x-10

y=[tex]\frac{4x}{3}-\frac{10}{3}[/tex]

is a required equation.

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