Write an equation of the line containing the given point and parallel to the given line. Express your answer in the form y=mx+b.
(-5,7);2x=9y+4
To find the equation of a line parallel to the given line, we need to determine its slope. First, let's rearrange the given line equation in slope-intercept form (y = mx + b).
2x = 9y + 4
Subtract 4 from both sides:
2x - 4 = 9y
Divide both sides by 9 to isolate y:
(2/9)x - 4/9 = y
Now we know that the slope of the given line is 2/9. Since the equation we're looking for is also parallel, it will have the same slope.
Using the point (-5, 7) and the slope 2/9, we can plug them into the point-slope form:
y - y1 = m(x - x1)
where (x1, y1) is the given point and m is the slope.
Substituting the values:
y - 7 = (2/9)(x - (-5))
Simplifying:
y - 7 = (2/9)(x + 5)
y - 7 = (2/9)x + (2/9) * 5
y - 7 = (2/9)x + 10/9
To express the equation in the desired form, we add 7 to both sides:
y = (2/9)x + 10/9 + 7
Simplifying:
y = (2/9)x + 10/9 + 63/9
Combining the fractions:
y = (2/9)x + 73/9
Therefore, the equation of the line containing the point (-5, 7) and parallel to the given line 2x = 9y + 4 is y = (2/9)x + 73/9.
To find an equation of a line parallel to the given line, we can use the fact that parallel lines have the same slope.
First, let's rewrite the given line in the slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.
2x = 9y + 4
Subtract 4 from both sides to isolate 9y:
2x - 4 = 9y
Divide both sides by 9 to solve for y:
(2x - 4)/9 = y
Now, we determine the slope of the given line. The slope is the coefficient of x in the slope-intercept form.
The slope of the given line is 2/9.
Since the parallel line should have the same slope, the slope of the parallel line is also 2/9.
Now, we can use the point-slope form of a linear equation to write the equation of the line. The point-slope form is given as:
y - y1 = m(x - x1),
where (x1, y1) is the given point and m is the slope.
The given point is (-5,7), so x1 = -5 and y1 = 7. Substituting the values, we get:
y - 7 = (2/9)(x - (-5))
Simplifying further:
y - 7 = (2/9)(x + 5)
Distributing the (2/9) on the right side:
y - 7 = (2/9)x + (10/9)
Adding 7 to both sides to isolate y:
y = (2/9)x + (10/9) + 7
Simplifying and combining terms:
y = (2/9)x + (10/9) + (63/9)
y = (2/9)x + 73/9
Therefore, the equation of the line containing the given point (-5,7) and parallel to the given line 2x = 9y + 4 is y = (2/9)x + 73/9.
y=-2x + 4
First put the equation 2x = 9y + 4 into slope-intercept form - you will basically be solving for y (y=mx+b). That will give you "m," which is your slope. Parallel lines have the same slope, so you now have your slope for your new line too.
Next, plug in all of your numbers to the equation y= mx+b. x and y are the points given to you that are in your new line: -5 and 7. Plug in your new slope for m. That leaves you with b to solve for. Solve for b.
Now use y = mx+b again. Substitute your slope for the m again and this time substitute your value for b into the equation, leaving the x and y in place. You now have your equation for your new line.