Answer:
The slope is -3/2.
Step-by-step explanation:
Hint: slope formula:
[tex]\displaystyle \frac{y_2-y_1}{x_2-x_1}=\frac{rise}{run}[/tex]
[tex]\displaystyle \frac{0-(-6)}{(-4)-0}=\frac{6}{-4}=\frac{6\div2}{-4\div2}=\frac{3}{-2}=-\frac{3}{2}[/tex]
[tex]\Large \textnormal{Therefore, the slope is -3/2.}[/tex]
Answer:
y=(-3/2)x+-6
or
y=(-3/2)x-6
Step-by-step explanation:
We are going to use slope-intercept form to find the equation for this line.
y=mx+b is slope-intercept form where m is the slope and b is the y-intercept.
y-intercept means where it crosses the y-axis; the x will be 0 here. Look the question gives us the y-intercept which is -6.
So we already know b which is -6.
y=mx+-6
Instead of finding the slope using the slope formula which you could.
I'm going to plug in the point (-4,0) into y=mx+-6 to find m.
So replace x with -4 and y with 0 giving you:
0=m(-4)+-6
0=-4m-6
Add 6 on both sides:
6=-4m
Divide both sides by -4:
6/-4=m
Reduce the fraction:
-3/2=m
The slope is -3/2.
Again you could use the slope formula which says [tex]m=\frac{y_2-y_1}{x_2-x_1} \text{ where } (x_1,y_1) \text{ and } (x_2,y_2) \text{ are points on the line}[/tex].
This is the same thing as lining the points up vertically and subtracting the points vertically then putting 2nd difference over first difference. Like this:
( 0 , -6)
-( -4 , 0)
---------------
4 -6
The slope is -6/4 which is what we got doing it the other way.
So the equation with m=-3/2 and b=-6 in y=mx+b form is
y=(-3/2)x+-6
or
y=(-3/2)x-6
