50POINTS!!!!!!Write an equation for all 4 lines showing in the graph in slope intercept formula (y= mx + b).

Line t: Notice that the line is horizontal. This means that it does not have a slope. The slope is 0 and the y-intercept is -4. Write the equation in the form y = mx+b and when you substitute, you get [tex]y=0(x)+4[/tex] , which means that [tex]y=4[/tex] is the correct equation.

Line m: Notice that the line is going down.This means the slope is negative. Look at how many units down the graph goes before it goes right and you will see that it is 2 units. The y-intercept will be 4 since this is where the graph crosses the y axis. Write the equation in the form y = mx+b and when you substitute, you get [tex]y=-2(x)+4[/tex], which means that [tex]y=-2x+4[/tex] is correct.

Line n: Notice that the line is going up.This means the slope is positive. Look at how many units up the graph goes before it goes right and you will see that it is 1 units. The y-intercept will be -1 since this is where the graph crosses the y axis. Write the equation in the form y = mx+b and when you substitute, you get [tex]y=1(x)-1[/tex], which means that [tex]y=x-1[/tex]

Line p: This one is a little tricky. Since it is a vertical line, we cannot write the equation of the line in terms of y since it is not a function and doesn't have a y-intercept. Therefore, we just locate the x-value that it crosses and write the answer in terms of x. Since the graph crosses the x-axis at [tex]x=-4[/tex] that will be the equation of the line.

That's it!

semsee45 semsee45 · Answer 2 · 2024-01-21T21:00:42+01:00

Answer:

[tex]\textsf{Line $l$:}\quad y = 4[/tex]

[tex]\textsf{Line $m$:}\quad y=-2x+4[/tex]

[tex]\textsf{Line $n$:}\quad y=x-1[/tex]

[tex]\textsf{Line $p$:}\quad x=-4[/tex]

Step-by-step explanation:

Line l is a horizontal line that is parallel to the x-axis. The equation for a horizontal line is y = c, where c represents the y-intercept of the line. Since line l crosses the y-axis at y = 4, the equation of line l is:

[tex]\Large\boxed{\boxed{\textsf{Line $l$:}\quad y = 4}}[/tex]

Line p is a vertical line that is parallel to the y-axis. The equation for a vertical line is x = c, where c represents the x-intercept of the line. Since line p crosses the x-axis at x = -4, the equation of line p is:

[tex]\Large\boxed{\boxed{\textsf{Line $p$:}\quad x=-4}}[/tex]

The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.

The slope (m) is defined as the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line, and the y-intercept (b) is the y-value of the point at which the line crosses the y-axis.

In line m, for every 1 unit of horizontal distance (run), the line decreases by 2 units vertically (rise). Therefore, the slope is m = -2. Line m intersects the y-axis at y = 4, so b = 4. Therefore, the equation of line m is:

[tex]\Large\boxed{\boxed{\textsf{Line $m$:}\quad y=-2x+4}}[/tex]

In line n, for every 1 unit of horizontal distance (run), the line increases by 1 unit vertically (rise). Therefore, the slope is m = 1. Line n intersects the y-axis at y = -1, so b = -1. Therefore, the equation of line n is:

[tex]\Large\boxed{\boxed{\textsf{Line $n$:}\quad y=x-1}}[/tex]