MATH SOLVE

4 months ago

Q:
# What is the equation of a line that is parallel to the line 2x + 5y = 10 and passes through the point (–5, 1)? Check all that apply. y = −x − 1 2x + 5y = −5 y = −x − 3 2x + 5y = −15 y − 1= −(x + 5)

Accepted Solution

A:

ANSWER[tex]2x+5y= -5[/tex]

EXPLANATIONIf the line whose equation we are finding is parallel to the line [tex]2x+5y=10[/tex] then it has the same slope as the slope of this line.

Let us write [tex]2x+5y=10[/tex] in slope intercept form;

[tex]\Rightarrow 5y=-2x+10[/tex]

[tex]\Rightarrow y=-\frac{2}{5}x+2[/tex]The slope of this line is [tex]-\frac{2}{5}[/tex] so the line whose equation we are finding also has slope [tex]-\frac{2}{5}[/tex].

Using the slope intercept form; the equation can be written as[tex]y=mx +c[/tex]

When we substitute the slope we get;[tex]y=-\frac{2}{5}x +c[/tex] Since the line passes through the point, [tex](-5,1)[/tex], it must satisfy its equation.

This implies that;[tex]1=-\frac{2}{5}(-5) +c[/tex]

[tex]1=2 +c[/tex]

[tex]-1=c[/tex]

Hence the equation is

[tex]y=-\frac{2}{5}x -1[/tex]

Multiplying through by 5 gives

[tex]5y=-2x -5[/tex]

Or[tex]5y+2x= -5[/tex]

EXPLANATIONIf the line whose equation we are finding is parallel to the line [tex]2x+5y=10[/tex] then it has the same slope as the slope of this line.

Let us write [tex]2x+5y=10[/tex] in slope intercept form;

[tex]\Rightarrow 5y=-2x+10[/tex]

[tex]\Rightarrow y=-\frac{2}{5}x+2[/tex]The slope of this line is [tex]-\frac{2}{5}[/tex] so the line whose equation we are finding also has slope [tex]-\frac{2}{5}[/tex].

Using the slope intercept form; the equation can be written as[tex]y=mx +c[/tex]

When we substitute the slope we get;[tex]y=-\frac{2}{5}x +c[/tex] Since the line passes through the point, [tex](-5,1)[/tex], it must satisfy its equation.

This implies that;[tex]1=-\frac{2}{5}(-5) +c[/tex]

[tex]1=2 +c[/tex]

[tex]-1=c[/tex]

Hence the equation is

[tex]y=-\frac{2}{5}x -1[/tex]

Multiplying through by 5 gives

[tex]5y=-2x -5[/tex]

Or[tex]5y+2x= -5[/tex]