The points (–1,–1) and (a,–5) fall on a line with a slope of 4. What is the value of a?
a=

The value of a is -2

Step-by-step explanation:

We are asked to give the value of a

We are provided with some information

We are given slope to be 4

And two points ( -1 ,-1) and

( a, -5)

Given the formula for slope

m = y_2 - y_1 / x_2 - x_1

Points ( -1 , -1)

(a, -5)

x_1 = -1

y_1 = -1

x_2 = a

y_2 = -5

Inserting the values given into

m = y_2 - y_1 / x_2 - x_1

= -5 - (-1) / a - (-1)

= -5 + 1 / a + 1

= -4 / a + 1

We are given the slope to be 4

i. e. m = 4

4 = -4 / a + 1

Cross multiply

4( a + 1) = -4

Open the bracket with 4

4a + 4 = -4

Collect like terms

4a = -4 - 4

4a = - 8

Divide both sides by 4 to get the value of a

4a / 4 = -8/4

a = -2

Therefore, x_2 = -2

the value of a = -2

example 2 – simplify: step 1: completely factor both the numerators and denominators of all fractions. step 2: change the division sign to a multiplication sign and flip (or reciprocate) the fraction after the division sign; essential you need to multiply by the reciprocal. step 3 : cancel or reduce the fractions.