Answer:
y=-2/7x-61/7
Step-by-step explanation:
convert to slope intercept form
2x+7y=9
7y=-2x+9
y=-2/7x+9/7
slope is -2/7
-7-2/7=-51/7
y=-2/7x-61/7
Answer:
[tex]y=-\frac{2}{7}x-\frac{51}{7}[/tex]
Step-by-step explanation:
Hi there!
We are given the line 2x+7y=9
We want to find the equation of the line that contains the point (-1, -7), and that is parallel to the equation above
Parallel lines have the same slopes.
So we need to find the slope of 2x+7y=9
One way to do this is to convert 2x+7y=9, which is currently in standard form (ax+by=c) into slope-intercept form, which is y=mx+b, where m is the slope and b is the y intercept.
In slope-intercept form, y is isolated by itself, so let's start by moving 2x to the other side (it removes it from the left side)
2x+7y=9
-2x -2x
____________
7y=-2x+9
Now divide both sides by 7
[tex]y=-\frac{2}{7} x + \frac{9}{7}[/tex]
in this equation, -2/7 is in the place of where m should be. This means that -2/7 is the slope of this line.
It is also the slope of the line parallel to it.
The instructions want us to write this equation in slope-intercept form, so let's plug -2/7 as m into the formula.
Here is the equation of the line so far:
[tex]y=-\frac{2}{7}x + b[/tex]
Now we need to find b.
As the equation contains the point (-1, -7), we can use it to help solve for b.
Substitute -1 as x and -7 as y into the equation
[tex]-7=-\frac{2}{7}(-1) + b[/tex]
Multiply
[tex]-7=\frac{2}{7} + b[/tex]
Subtract 2/7 from both sides
[tex]-\frac{51}{7} = b[/tex]
Substitute -51/7 as b in the equation
[tex]y=-\frac{2}{7}x-\frac{51}{7}[/tex]
Hope this helps!
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