Exercise 1 Page 242

a We have been given three equations. We need to determine whether or not each equation represents a line with slope m=5 and contains the point (3,8). Let's begin with the first equation.

5x-y=7 We can rewrite the equation in the slope-intercept form,

y= mx+ b, where m is the slope and b is the y-intercept, in order to see the slope more clearly.

5x-y=7

SubEqn

LHS-5x=RHS-5x

- y=-5x+7

DivEqn

.LHS /(-1).=.RHS /(-1).

y=5x-7

Now we can see that the equation does satisfy the condition that m=5. Let's check if it contains the point (3,8) by substituting it into the equation.

y=5x-7

SubstituteII

x= 3, y= 8

8? =5( 3)-7

Multiply

8? =15-7

SubTerm

Subtract term

8=8

Since the point satisfies the equation, it is contained on the line. Therefore, this equation satisfies both conditions.

b Next, let's take a look at the second equation.

3x+8y=5 Just as in Part A, let's rewrite this equation in slope-intercept form.

3x+8y=5

SubEqn

LHS-3x=RHS-3x

8y=-3x+5

DivEqn

.LHS /8.=.RHS /8.

y=-3/8x+5/8

The equation does not satisfy the condition that m=5. Therefore, we do not need to check the second condition because we already know it does not fit the requirements.

c Finally, let's check our last equation.

10x-2y=14 One more time, let's find the slope by rewriting the equation in the slope-intercept form.

10x-2y=14

SubEqn

LHS-10x=RHS-10x

- 2y=-10x+14

DivEqn

.LHS /(-2).=.RHS /(-2).

y=5x-7

This equation is exactly the same equation as we found in Part A. Therefore, we already know that it will satisfy both conditions.

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Exercise 1 Page 242

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