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slope-intercept form

3.1-72 Graph the line defined by the equation .
Find the y values for the following values of x:
When x = -7:
-7 + 4y = 5
4y = 12
y = 3

When x = -3:
-3 + 4y = 5
4y = 8
y = 2

When x = 1:
1 + 4y = 5
4y = 4
y = 1

When x = 5:
5 + 4y = 5
4y = 0
y = 0

When x = 9:
9 + 4y = 5
4y = -4
y = -1

x y
-7 3
-3 2
1 1
5 0
9 -1

3.1-84 Graph the equation using the x-and y-intercepts. Uset a third point to check.

For finding x-intercept, put y = 0
-2x = 4
x = -2
x-intercept is (-2, 0)

for finding y-intercept, put x = 0
y = 4
y-intercept is (0, 4)

A third point on graph of line is (-1, 2) and it also satisfies the equation
-2x + y = 4.

3.2-38 Find the slope of the line that goes through (-0.1, 0.2) and (0.5, 0.8).

Slope = =1

3.2-42 Graph the line through (-2, 5) with slope of -1.

3.3-30 Find the slope and y-intercept, if they exist, for the line .

Solve equation for y
x - y = 4
-y = -x + 4
y = x - 4

Slope = 1, y-intercept: (0, -4)

3.3-82 Write an equation in slope-intercept form, if possible for the line through
(0, -1) that is perpendicular to the line .

Slope of perpendicular line will be -1.

Equation of line will be

y - (-1) = -1(x - 0)
y + 1 = -x
y = -x - 1

3.4-22 Find the equation of the line through (-3, 1) with slope -1/3. Write answer in slope intercept form.

Equation of line will be

y - 1 = -(1/3)(x - (-3))

y - 1 = -(1/3)x - 1

y = -(1/3)x

3.4-50 Find the equation of the line parallel to that goes through the point (-3, 6). Write answer in slope-intercept form.

Slope of parallel line will be -1.

Equation of line will be

y - 6 = -1(x - (-3))
y - 6 = -x - 3
y = -x + 3

3.5-14 Write a foumula that expresses the relationship describe by the statement "t is inversely proportional to e." Use k as the constant.

3.5-34 Gas Laws. The volume of a gas is inversely proportional to the pressure on the gas. If the volume is 6 cubic centimeters when the pressure is 8 kilograms per square centimeter, then what is the volume when the pressure is 12 kilograms per square centimeter?

Let the volume be V and pressure be P

If the volume is 6 cubic centimeters when the pressure is 8 kilograms per square centimeter

Now, cubic centimeters

3.6-2 How can you tell if an ordered pair satisfies a linear inequality in two variables?

We substitute the values of coordinates in linear inequality to check if it satisfies the linear inequality or not.

3.6-10 Determine which of the following points satisfy .

Check for (-2, 6)
2x + y = 2*(-2) + 6 = -4 + 6 = 2 < 3

Thus, (-2, 6) satisfies the inequality.

Check for (0, 3)
2x + y = 2*0 + 3 = 3 which is not less than 3

Thus, (0, 3) does not satisfy the inequality.

Check for (3, 0)
2x + y = 2*3 + 0 = 6 which is not less than 3

Thus, (3, 0) does not satisfy the inequality.

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3.1-72 Graph the line defined by the equation .
Find the y values for the following values of x:
When x = -7:
-7 + 4y = 5
4y = 12
y = 3

When x = -3:
-3 + 4y = 5
4y = 8
y = 2

When x = 1:
1 + 4y = 5
4y = 4
y = 1

When x = 5:
5 + 4y = 5
4y = 0
y = 0

When x = 9:
9 + 4y = 5
4y = -4
y = -1

x y
-7 3
-3 2
1 1
5 0
9 -1

3.1-84 Graph the equation using the x-and y-intercepts. Uset a third point to check.

For finding x-intercept, put y = 0
-2x = 4
x = -2
x-intercept is (-2, 0)

for finding y-intercept, put x = 0
y = 4
y-intercept is (0, 4)

A third point on graph of line is (-1, 2) and it also satisfies the equation
-2x + y = ...

Solution Summary

This solution answers various questions involving slope and intercepts.

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