Math help ??? Slope & Equation?

Question

1> Find an equation of the line having the given slope and containing the given point.

m=3, (3,2) Equation of the line is y= ???

2> Find the slope if it exists, of the line containing the pair of points.

(8,3) and (9, -5)

3> Find the slope of the line y= 3

The slope is ???

4> Find an equation of the line having the given slope and containing the given point m= -5(2,4) * type using y=mx + b format

y = ???

Answer 1

1. m=3, (3,2)

Use the point-slope equation: y-y1 = m(x-x1)

x1 = 3

y1 = 2

y-2 = 3(x-3)

y = 3x - 9 + 2

.: y = 3x -7

2. Find the slope if it exists, of the line containing the pair of points: (8,3) and (9, -5)

m = (y2-y1)/(x2-x1) which is translated as "rise over run"

Substitute the values from the ordered pairs:

m = (-5-3)/(9-8) = -8/1

.: m = -8

The slope of the line containing the given points is -8.

3. Find the slope of the line y = 3

The point-slope form is y = mx + b.

Since y = 3, then m must be 0 because y = 0x + 3. Hence, the slope is 0 and the line is horizontal.

4. Find an equation of the line having the given slope and containing the given point m= -5 (2,4) * type using y=mx + b format

Use again the point-slope equation, substituting the values.

y-4 = -5(x-2)

y = -5x + 10 + 4

.: y = -5x + 14

Answer 2

Point-slope form gives the equation of a line passing through a point (x1, y1) and having the slope m as:

y - y1 = m(x - x1)

In the first question you are given that the slope m = 3 and the point (3, 2). Substitute x1 = 3 and y1 = 2 into the equation above to find the equation of the line as:

y - 2 = 3(x - 3)

If you want, you can rewrite this in slope-intercept form by solving for y.

y - 2 = 3x - 9

y = 3x - 9 + 2

y = 3x - 7

For the second question, the slope of a line through points (x1, y1) and (x2, y2) is given by

m = (y1 - y2) / (x1 - x2)

In your case, the line contains the points (8,3) and (9,-5)

m = (3 - (-5)) / (8 - 9)

m = (3 + 5) / (-1)

m = -8

For the third question the line y = 3 is horizontal so the slope is zero.

For the final question use the point-slope form mentioned in the first question and solve the equation for y.

y - y1 = m(x - x1)

y - 4 = -5(x - 2)

y - 4 = -5x + 10

y = -5x + 10 + 4

y = -5x + 14

Hope this helps you!