# Equation of a straight line.

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1. Find the equation of the line described in each case:

a) Gradient 3, cuts through (0, 6).

b) Steepness of 4, passes through (0, -2).

c)Parallel to y = 5x - 1, cuts the y-axis at (0, 10).

d)Cuts through (0, 7) and (5, 17)

2. Here are 3 eqautions:
A. y + 1 = 3x
B. y = -3(x - 1)
C. 2y = 8x + 6

Find the odd one out in each case:
b) Slopes in a positive direction
c) Cuts the y-axis at (0, 3)

3. A line passes through the point (10, 10). It's equation is y = mx + 4. Find the value of m.

I'll try to get you started on these, and let you take it from there.

For 1a:
y - y1 = m(x - x1)
y - 6 = 3(x - 0)
y - 6 = 3x
y = 3x + 6

For 1b:
Use the same procedure as 1a.

For 1c:
Parallel lines have the same slope.
y - 10 = 5(x - 0)
I'll let you finish.

For 1d:
m = (y2 - y1)/(x2 - x1)
m = (17 - 7)/(5 - 0)
m = 10/5 = 2
Therefore, using the first ordered pair (0, 7), we have this:
(y - 7)/(x - 0) = 2
y - 7 = 2(x - 0)
I'll let you take it from here to finish.

For 2a:
The coefficient of x is the slope.

For 2b:
Look for positive slopes.

For 2c:
Substitute 0 for x and 3 for y in each equation to check each one.

For 3:
Substitute 10 for x and 10 for y. Solve the equation for m, which is the slope.

I hope this will help get you started on these problems.

<<3. A line passes through the point (10, 10). It's equation is y = mx + 4. Find the value of m>>
Since y = mx + 4 and y = 10 when x = 10, plug those values of x and y into the eqwuation and solve for m.