Line L in the figure below is parallel to the line y = 4 x + 1. Find the coordinates of the point P

To figure out what "b" is, it is shown that point (0, -2) is on line L. So plug that into y = 4x + b, and we will see that b has to be equal to -2. Thus our equation of L is: y = 4x - 2

Now since P is a x-intercept, it has the coordinates: (x,0).

To figure out what x is, we need to solve:

0 = 4x - 2, solve:

2 = 4x

2/4 = x

1/2 = x

Thus point P is (1/2,0)

MrRoyal MrRoyal · Answer 2 · 2021-09-17T19:20:10+02:00

The figure is an illustration of a linear graph, where the coordinates of point P is (0.5,0)

From the figure:

Line L is parallel to the line with equation [tex]y = 4x + 1[/tex]

This means that they have the same slope

A linear equation is represented as:

[tex]y = mx + b[/tex]

Where

[tex]m \to slope[/tex]

So, the slope of [tex]y = 4x + 1[/tex] and line L is 4

Point P is on the line of the x-axis; so, the coordinate of point P is (x,0)

On line L, we have the following points: (x,0) and (0,-2)

The slope (m) of a line is calculated using:

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

So, we have:

[tex]4 = \frac{-2 - 0}{0 - x}[/tex]

[tex]4 = \frac{-2}{- x}[/tex]

[tex]4 = \frac{2}{x}[/tex]

Make x the subject

[tex]x = \frac{2}{4}[/tex]

[tex]x = 0.5[/tex]

Hence, the coordinate of point P is (0.5,0)