Respuesta :

Answer:

y=(5/2)x+(-11/2)

Problem: What is the slope-intercept form for a line going through (3,2) and is parallel to y=(5/2)x-5?

Step-by-step explanation:

Parallel lines have the same slope.

The slope-intercept form of a line is y=mx+b where m is the slope and b is the y-intercept. So we see that m=5/2 since that is the slope of y=5/2 x-5.

y=(5/2)x+b

We know (x,y)=(3,2) is a point on the line so replacing x with 3 and y with 2 gives:

2=(5/2)(3)+b

2=(15/2)+b

Subtract 15/2 on both sides:

2-(15/2)=b

Simplify:

(4-15)/2=b

(-11/2)=b

So the equation is:

y=(5/2)x+(-11/2)

luisejr77

Answer:

[tex]y=\frac{5}{2}x-\frac{11}{2}[/tex]

Step-by-step explanation:

The equation of a line has the following form:

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

Where m is the slope of the line and b is the intercept with the y axis.

If two lines of slopes m and n are parallel  then it is true that:

[tex]m=n[/tex]

For the line [tex]y =\frac{5}{2}x-5[/tex] the slope is: [tex]m=\frac{5}{2}[/tex]

So the slope of the parallel line is:

[tex]m=\frac{5}{2}[/tex]

So the equation is:

[tex]y=\frac{5}{2}x+b[/tex]

To find b we substitute the point (3, 2) in the equation and solve for b

[tex]2=\frac{5}{2}(3)+b[/tex]

[tex]b=2-\frac{15}{2}[/tex]

[tex]b=-\frac{11}{2}[/tex]

Then the equation of the line in the form of pending interception is:

[tex]y=\frac{5}{2}x-\frac{11}{2}[/tex]