Question

How would I do this equation with a fraction in it?

Answer 1

Given:

Equation of line

`y+4=-(3)/(2)(x-7)`

And a point (1,2).

Required:

To find the equation of the line that is parallel to the given line and passes through from the given point.

Step-by-step explanation:

The given equation is:

`y+4=-(3)/(2)(x-7)`

Write the equation in slope-intercept form y= mx+b.

`\begin{gathered} y+4=-(3)/(2)x+(21)/(2) \\ y=-(3)/(2)x+(21)/(2)-4 \\ y=-(3)/(2)x+(21-4*2)/(2) \\ y=-(3)/(2)x+(13)/(2) \end{gathered}`

Compare this equation with y=mx+b, we get

`m=-(3)/(2)`

The slope of the parallel lines is equal. So the line that is parallel to the given lime has the same slope.

The equation of line has slope m and passes through from the point

`(x_1,y_1)`

is given by the formula:

`y-y_1=m(x-x_1)`

Thus the equation of the line passes through from the point (1,2) and has slope m= -3/2 is:

`\begin{gathered} y-2=-(3)/(2)(x-1) \\ y-2=-(3)/(2)x+(3)/(2) \\ y=-(3)/(2)x+(3)/(2)+2 \\ y=-(3)/(2)x+(3+2*2)/(2) \\ y=-(3)/(2)x+(7)/(2) \end{gathered}`

Final Answer:

The equation of the line that is parallel to the given line and passes through from the point (1,2) is

`y=-(3)/(2)x+(7)/(2)`