Question

What is the equation of a line that passes through (7, 8) and has a slope of -3?

A.
`y = -3x + 29`
Select the correct answer from each drop-down menu.


Points A, B, and C form a triangle. Complete the statements to prove that the sum of the interior angles of ΔABC is 180°.

Statement Reason
Points A, B, and C form a triangle. given
Let be a line passing through B and parallel to . definition of parallel lines
∠3 ≅ ∠5 and ∠1 ≅ ∠4
m∠1 = m∠4 and m∠3 = m∠5
m∠4 + m∠2 + m∠5 = 180° angle addition and definition of a straight line
m∠1 + m∠2 + m∠3 = 180° substitution

B.
`y = 3x + 13`

C.
`y = (1)/(3)x− 29`

D.
`y = -(1)/(3)x− 13`

Answer 1

A. `y = -3x + 29`

Explanation:

The equation of a line is expressed as y = mx + c where m is the slope of the line and c is the intercept.

The slope of the line is given as -3.

So the equation can be represented as y = -3x + c

The line passes through point (7,8)

=> 8 = -3(7) +c

=> 8 = -21 + c

=> c = 8 + 21 = 29

Substituting in the original equation of the line:

y= -3x + 29

Validation: Substituting x= 7 and y=8 in the equation:

8 = -3 * 7 + 29

Or 8 = 8

So the two sides are equal and our equation is valid.

Answer 2

Equation A

Step-by-step solution:

According to the general equation for a line,

y=mx+b

where m is the slope and b is the interception with the y axis.

Comparing to all of the options only option A has a slope m=-3.

Even more, if we substitute x=7 into this equation the corresponing y value is 8, as initially requested.

y= - 3(7)+29= - 21+29=8