Question

Suppose a line passes through (a, -11) and (7,13), and is parallel to the line

Answer 1

Answer:

a=19

Step-by-step explanation:

The slope of the equation is - 2 as it's parallel to the given line. Using two point slope form, (13-(-11))/(7-a)=-2. 24=-2(7-a), - 12=7-a, a=19

Answer 2

Answer:

see explanation

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 2x + 8 ← is in slope- intercept form

with slope m = 2

Parallel lines have equal slopes

Calculate the slope between the 2 given points and equate to 2

Using the slope formula

m = $\frac{y_{2}-y_{1} }{x_{2}-x_{1} }$

with (x₁, y₁ ) = (a, - 11) and (x₂, y₂ ) = (7, 13)

m = $\frac{13-(-11)}{7-a}$ = $\frac{13+11}{7-a}$ = $\frac{24}{7-a}$ , then

$\frac{24}{7-a}$ = 2 ( multiply both sides by 7 - a )

2(7 - a) = 24 ( divide both sides by 2 )

7 - a = 12 ( subtract 7 from both sides )

- a = 5 ( multiply both sides by - 1 )

a = - 5

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y = 2x + c ← is the partial equation

To find c substitute (7, 13) into the partial equation

13 = 14 + c ⇒ c = 13 - 14 = - 1

y = 2x - 1 ← equation of parallel line