Question

Graph the linear equation and answer each of the following questions. y=-2x-3

Answer 1

Answer:

Part 1) The y-intercept is the point (0,-3)

Part 2) The slope in fraction form is $m=-\frac{2}{1}$

Part 3) The graph in the attached figure

Step-by-step explanation:

we have

$y=-2x-3$

Part 1) What is the y-intercept?

Remember that

The y-intercept is the value of y when the value of x is equal to zero

so

For x=0

substitute in the linear equation and solve for y

$y=-2(0)-3\\y=-3$

The y-intercept is the point (0,-3)

Part 2) What is the slope (in fraction form)?

we have

$y=-2x-3$

This is the equation of the line in slope intercept form

$y=mx+b$

where

m is the slope or unit rate

b is the y-intercept

so

$m=-2$

In fraction form is

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

The slope is negative, that means, is a decreasing function (as the x-values increases the y-values decreases)

Part 3) Graph the line

To graph the line we need two points

From the y-intercept (0,-3) use the slope to find your next point

The slope is -2, so you will rise -2 (2 units down) and run 1 (1 unit to the right).

The next point is (0+1,-3-2) -----> (1,-5)

so

Plot the points (0,-3) and (1,-5), connect them and graph the line

The graph in the attached figure