Question

A line passes through the points (–1, –5) and (4, 5). The point (a, 1) is also on the line.

Answer 1

Answer: $a=2$

Step-by-step explanation:

We know that this line passes through the point $(a,1)$ where "a" is the  unknown x-coordinate of that point and 1 is the y-coordinate.

We also know that this line passes through the points (-1, -5) and (4, 5).

Then, in order to find the value of "a", we can plot the known points and draw the line (Observe the image attached).

You can observe in the image attached that the point whose y-coordinate is 1 is the point (2,1). Therefore, the value of "a" is:

$a=2$

Answer 2

Answer:

a = 2

Step-by-step explanation:

Let's find the equation of the line using the 2 points given.

Let's call -1 as x_1 and -5 as y_1

also, 4 as x_2 and 5 as y_2

The equation of line is :

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

Let's plug the points and get the equation of the line:

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)\\y+5=\frac{5+5}{4+1}(x+1)\\y+5=2(x+1)\\y+5=2x+2\\y=2x-3$

Now, to find a, we substitute a in x and 1 in y of the equation of the line we just got:

$y=2x-3\\1=2(a)-3\\1=2a-3\\2a=4\\a=\frac{4}{2}=2$