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

Answer 1

You are given that the line in question passes through two points, (-1,0), the x intercept, and the given point (1, -3). The slope of the line is given by

m=(y2-y1)/(x2-x1) so m=(-3-0)/(1-(-1)) which simplifies to m = -3/2

Now, use the point/slope formula using either of the given points

(y-y1) = m*(x-x1).

(y-0) = (-3/2)*(x-(-1)) or y=(-3/2)x - (3/2)

Answer 2

What do you want to find from this? Given the x-intercept, you now have a second point of (-1,0). With these two points you can find the slope given the formula:

m = y₂ - y_1/x₂ - x₁

Once you have the slope, you can use the slope intercept form, y = mx + b, to find the b, the y-intercept.

Hope this helps. If you want me to go through the actual calculations, let me know.

Answer 3

Are you talking about a straight line?

If so, then you have 2 points on the line: (1,-3) and (-1,0) (the latter is the definition of "x intercept"--where y = 0)

You can use the "slope-intercept" equation: y = mx + b, where m is the slope and b is the y intercept, where x = 0.

Create 2 equations using the given points:

-3 = m*1 + b

0 = m*-1 + b

Put in standard form:

m + b = -3

-m + b = 0

Add the two equations:

2b = -3, so b = -3/2

From either equation, we then have m = -3/2

So...the equation of the line is y = (-3/2)*x - 3/2

Answer 4

Hello Hector,

I assume that you want to find the equation of the line that passes through the point (1,-3) and has x-intercept -1. (If this is not what you actually needed to find, let me know.)

The problem indicates that the x-intercept = -1, which is the same as saying the line contains the point (-1,0). Now we can use the two points (1,-3) and (-1,0) to find the slope.

m = (y₂ - y₁)/(x₂ - x₁)

m = (0 - (-3))/((-1 - 1)

m = 3/(-2) = -3/2

Now use the point-slope form to find an equation of the line.

y - y₁ = m(x - x₁)

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

Generally, we prefer to express the final answer in either slope-intercept form (y = mx + b form), or standard form (Ax + By = C). To put the equation in slope-intercept form, we solve the above for y.

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

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

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

Hope that helps!

William