help with math!?

Question

1.) write an equation in slope-intercept form for the line with a slope of -1/3 and x intercept 3

2.)write an equation in slope intercept form of the line passing through the points (-3,-1) and (1,-4)

Answer 1

1.) -1/3x + 3
y-intercept you mean?
cause i forget how to do x-int.
2.) formula: y2-y1 / x2-x1

-1- -4 / -3 - 1

3/-4 is your slope (-3/4)

draw it on graphing paper to get the y-int.

Answer 2

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

x-intercept is the value of x value of the line when it intersects the x-axis. Your line intersects the x-axis when y is zero. Hence, the x-intercept is the value of your x when your y is zero. So we know that when y=0, x=3.

Since the slope is -1/3... we write the equation:

y = (-1/3)x + b
but we don't know yet the y-intercept. Since we know that y=0 when x=3, we replace the variables with the values.

0 = (-1/3)(3) + b
0 = -1 + b
1 = b

Hence the y-intercept is 1.
So we write the complete slope-intercept form of the equation:

y = (-1/3)x +1

Problem 2. Given two points, we can easily find the slope using the equation m=(y2-y1)/(x2-x1) where (x1, y1) and (x2, y2) are points where the line passes through.

Hence the slope of the line is [-4-(-1)] / [1-(-3)]
=(-4+1)/(1+3) = -3/4

So the slope of the line is -3/4.
So we can also write the linear equation as y-y1=m(x-x1)
So the linear equation is y-(-1) = (-3/4)(x - (-3)
which gives: y +1 = (-3/4)(x + 3)
and thus yields y+1 = (-3/4)x -9/4

we transform this equation into slope intercept form
y = (-3/4)x - 9/4 - 1
and equivalently
y = (-3/4)x -13/4

Answer 3

y = mx + b and b = -1/3 do
y = (-1/3)x + b x-intercept => y = 0 so
0 = (-1/3)*3 + b => b = 1 and final equation is
y = (-1/3)*x + 1

Slope is
(-4 - (-1))/(1 - (-3)) = (-3)/(4) = -.75 so
y = -.75*x + b and at (1,-4)
-4 = -.75*(1) + b => b = -3.25 so
y - -.75*x - 3.25

HTH ☺

Doug

Answer 4

1. y=-1/3x+1
2. y=-4/3x-13/3

Answer 5

1) x = -3y + 3
or, y = (-1/3)x +1

2) y-(-1) = {-4 - (-1)}/{1 - (-3)}{x-(-3)}
or, y= (-3/4)x - 13/4