I need some help with point-slope and slope-intercept form?

Question

Use the given conditions to write an equation for each line in point-slope form and slope-intercept form:

Passing through (1,-3) with x-intercept = -1.

Answer 1

Slope-intercept
y = mx + b,
To write this one, you need m, the slope
and b, the y-intercept defined as point (0,b)

Point-slope
y - y1 = m(x - x1)
To write this, you still need m,
but you can use any point on the line for (x1 , y1)


They give you a point and the x-intercept, which is actually another point. The x-intercept is a point where y = 0, so it's really (-1,0)

Two points give the slope: m = (y2 - y1)/(x2 - x1)
(0 - (-3)) / (-1 - 1) = 3/-2 = -(3/2)

You don't have a y-intercept, so use the point-slope formula:

y - (-3) = -(3/2)(x - 1)

Then rearrange it to look like slope-intercept form:

y + 3 = -(3/2)x + (3/2)
y = -(3/2)x + (3/2) - 3
y = -(3/2)x - (3/2)

Answer 2

You know that interccept's form is x/a + y/b = 1
I think you know that a is x-intercept and b is y intercept.
Substitute the x-intercept here. And also the point in the equation.

1/-1 - 3/b = 1 this gives 3/b = -2
Which gives b= -3/2

Substitute the values of a and b in interccept's form. Which gives
-x - 2y/3 = 1 gives x + 2y/3 = -1 gives 3x + 2y = -3

So the line equation is 3x + 2y = -3.

Slope intercept form is y = mx + c
From the above equation we can write that y = -3x/2 - 3/2
Here slope is -3/2 and y-intercept is -3/2.

Similarly you can find the point slope form.

Hope you understood this.

Answer 3

There are lots of equation of lines.

Given a slope m and point (x0,y0), an equation of the line containing the point with specifiied slope is

y-y0=m(x-x0). This is point slope form of a line.

y=mx+b is usually called the slope intercept form.

For you,

y(1)=-3 so

3=m(x-1) (A)

Because the x-intercept is -1, we know that (-1,0) is on the line too. Thus,

0=m(x+1) (B)

Solving (A) and (B) for m and x gives us

x=-1 and m=-3/2.

That is a really neat problem! :)

Answer 4

Slope of a Line: If a line passes via 2 distinctive factors P1(x1 , y1) and P2(x2, y2), its slope is given via: m = (y2 - y1) / (x2 - x1) with x2 no longer equivalent to x1. that's yet another interactive academic on the slope of a line. Slope intercept style of a Line: The equation of a line with a defined slope m is additionally written as follows: y = mx + b the place m is the slope of the line and b is the y intercept of the graph of the line. The above type is talked approximately as the slope intercept style of a line. to understand why, bypass to this interactive academic.

Answer 5

So X intercept = -1 means you have a point (-1,0)

Using those two points, you make the slope

M = (y2-y1)/(x2-x1)=(0-[-3])/(-1-1) = -3/2

Now use the equation y-y' = m(x-x') Where y' and x' is either one of the two sets of points you have:

y+3 = -3/2(x+1) and then solve:

y = -3/2x - 3/2 + 3 = -3/2x + 3/2

Answer 6

formula for any line is :y=mx+c
c=sqrt(x^2+y^2);for any line c continuously changes hence its a line.thus c=0 at origin.

Answer 7

i think the formula is (y - y1)=m(x-x1)