Lets do the first one(7). Fist change 10x -2y = 3,which is in standard form to point slope form so you can see the slope.
10x - 2y = 3
-2y = -10x + 3
-2y/-2 = -10x / -2 + 3/-2
y = 5x - 3/2
The slope is the m in y = mx + b so our slope is 5x, well it wants you to find the equation of a line that passes through (0,1) that is parallel to the equation this (Parallel) mean has the same slope.The slope is 5. Now that we know the slope is 5 we can find the equation by using the point slope form of an equation of a line.
point slope form = y – y1 = m(x – x1)
Remember m = slope = 5. Now plugin our x and y cord from the point (0,1) and our slope of 5
y - y1 = m(x - x1)
y - 1 = 5(x - 0)
y - 1 = 5x - 0
y - 1+1 = 5x + 1
y= 5x + 1
So the point (0,1) passes through y = 5x + 1
Number 8 is already in slope intercept form so you don't have to do anything to find the slope. You can see that the slope is 7 so just plug your point into y - y1 = m(x - x1) and then put it into slope intercept form.
8)
Point = (5,8)
Slope = 7
y - y1 = m(x - x1)
y - 8 = 7(x - 5)
y = 7x - 27
So for number 8 the point (5,8) passes through y = 7x - 27
(9) For nine they want an equation that is perpendicular, which means to flip the slope. For instance, if you have a slope of 2/5 the perpendicular slope would be 5/2. For 9 we see that the slope is 2/5 so its perpendicular slope would be 5/2. Now just plug your point into the point slope form equation.
Point = (-4, 6)
Slope = 2/5
perpendicular slope = 5/2
y - 6 = 5/2(x - (-4))
y = 5/2 x + 16
So point (-4, 6) passes through y = 5/2 x + 16
(10) Point (4,1) passes through y = 7/5 x - 23/5
