Write a equation of the line containing the given point and paralled to the given line (-5,8);3x=5y+2
5y = 3 x - 2
y = (3/5) x - 2/5
so slope = 3/5
8 = (3/5)(-5) + b
8 = -3 +b
b = 11
so
y = 3 x/5 + 11
or
5 y = 3x + 55
Parallel to 3x = 5y + 2
through P(-5,8)
Parallel lines have equal slopes
First, you need to put the given line in slope-intercept form, to find the slope.
Slope-intercept form,
y = mx + b
m = slope
b = y-intercept
3x = 5y + 2
To put in slope-intercept form, solve for y.
3x = 5y + 2
5y = 3x - 2
y = 3/5 x - 2/5
So now you know that the slope m = 3/5.
y = 3/5 x - 2/5
y = mx + b
Since parallel lines have the same slope, 3/5 will be the slope of your line through (-5,8)
y = mx + b
y = 3/5 x + b
Now you need to use the point (-5.8)
Since x = -5 and y = 8, put those value in your equation.
y = 3/5 x + b
8 = 3/5 (-5) + b
All that's left is too solve for the b value.
8 = 3/5 (-5) + b
8 = -15/5 + b
8 = -3 + b
b = 11
Now you have all you need for your parallel line
y = mx + b
slope m = 3/5
b = 11
y = 3/5 x + 11
Do you follow what I've done?
Good luck
Thank you very much for your quick answer and for your time. However, I am still confused about how to get the top number on the left. For instance, the 11, or 55. What do you multiply, add, or divide?
Can you please use this one to show me step by step how you work out this problem? (-8,6);2x=3y+4 I can get the first part, however, I can't figure how to work the last part of the problem. I really do appreciate your help, thank you.
To find the equation of a line parallel to another line, we need to know that parallel lines have the same slope.
For the given line, 3x = 5y + 2, we can rearrange it into slope-intercept form (y = mx + b) to determine its slope.
3x = 5y + 2
5y = 3x - 2
y = (3/5)x - 2/5
So, the slope of the given line is 3/5.
Now we have the slope (m) of the line we want to find and a point (-5, 8) that it passes through. We can use the point-slope form (y - y1 = m(x - x1)) to build the equation of the line.
Substituting the slope (m = 3/5) and the point (-5, 8) into the point-slope form:
y - 8 = (3/5)(x - (-5))
y - 8 = (3/5)(x + 5)
Now, we can simplify this equation further:
y - 8 = (3/5)x + 3
y = (3/5)x + 3 + 8
y = (3/5)x + 11
Therefore, the equation of the line containing the given point (-5, 8) and parallel to the line 3x = 5y + 2 is y = (3/5)x + 11.