I purchased an Algebra exercise book to help me and I need help with this question

## Choose the equation below that represents the line passing through the point (-3, -1) with a slope of 4.

# 3 Answers

ya we will use the simple formula and put the points (-3,-1) in that formula y-y_{1
}=m(x-x_{1})

so, here x_{1 }=-3 and y_{1 }=-1 and m=4 so, simply by putting the values we get...

y-(-1)=4(x-(-3))

y+1=4(x+3)

y=4x+12-1

y=4x+11

Hi Amy... I'll add:

The slope is the x-coefficient, or x-multiplier. From our sample problem, we know we have one term, 4x

We also know that when we have a set of points from a graph, then we have an x-y coordinate (location) that gives us both x and y at the same time (same place on the equation graph), and both can be plugged into the equation.

Coordinates are usually given as (x, y), and from our sample we have x = -1, and y = -3. Now we can just plug these into the standard
**y = mx + b** format for a linear (straight line) equation: -1 = 4(-2) + b.

"b" is the value y has when x = 0; you can think of it as a y-offset above or below zero, because if b = 0, then when x = 0, y would also = 0, and our line would pass through (0, 0).

(y = m(0) + 0; y = 0). We can find b by solving y=mx+b for b: **b = y - mx**.

In our sample, b = (-1) - (4)(-3); b = -1 + 12, so b = +11. **Our final equation: y = 4x + 11**

To prove it: y = 4(-3) + 11; y = -12 + 11 = -1, which is the original y-coordinate :-)

There is a formula well-known as the point-slope equation. It gives the equation of the line through a given point with a given slope. Here it is:

y - y_{1} = m(x - x_{1}),

where (x_{1}, y_{1}) is the given point and m is the slope.

I hope this helps. If you would like more assistance, please feel free to ask. I or another tutor will be happy to assist you.