So the right options are:
[tex]y=-\frac{2}{5}x-1[/tex]
[tex]2x+5y = -5[/tex]
[tex]y-1=-\frac{2}{5}(x+5)[/tex]
Further explanation:
Given equation of line is:
2x+5y=10
We have to convert it into point-slope form
[tex]2x+5y=10\\5y=-2x+10\\Dividing\ both\ sides\ by\ 5\\y=-\frac{2}{5}x+\frac{10}{5}\\y=-\frac{2}{5}x+2[/tex]
The co-efficient of x is the slope of the line
So,
[tex]m= -\frac{2}{5}[/tex]
As the required line is parallel to given line, it will also have same slope.
Let m1 be the slope of required line
Then the line will be:
[tex]y=m_1x+b[/tex]
Putting the value of slope
[tex]y=\frac{2}{5}x+b[/tex]
Putting (-5,1) in the equation to find the value of b
[tex]1=-\frac{2}{5}(-5)+b\\1=2+b\\b=1-2\\b=-1[/tex]
Putting the values of slope and b in equation
[tex]y=-\frac{2}{5}x-1[/tex]
Multiplying the whole equation by 5 will give us:
5y = -2x-5
2x+5y = -5
Another form of equation of line is Point-slope form
[tex]y-y_1=m(x-x_1)[/tex]
Putting the values of slope and point in the equation, we get
[tex]y-1=-\frac{2}{5}(x+5)[/tex]
So the right options are:
[tex]y=-\frac{2}{5}x-1[/tex]
[tex]2x+5y = -5[/tex]
[tex]y-1=-\frac{2}{5}(x+5)[/tex]
Keywords: Point-Slope form, Parallel lines
Learn more about point slope form at:
#LearnwithBrainly
Answer:
Step-by-step explanation:
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 = −Two-fifthsx − 1
2x + 5y = −5
y = −Two-fifthsx − 3
2x + 5y = −15
y − 1= −Two-fifths(x + 5)
The answer? All that apply A B and E
