Liner Equations

Linear Equations is an algebra equation where each term is has exponent of 1.

Linear equations always use the equal sign(=). Moreover, when graphed the line(s) is always straight.

Below is the equation of a straight line…

y = mx + b

We title this slope intercept form

Sometimes, well be asked to find the m and b of the line.

m is our slope or rise over run rise/run

Plus! There are different types of slope postive, negative, zero, and undefined

• We need to know this to graph and solve or slopes, as the word slope is the steepness of and direction of a line.

To find or solve rise over run we use the slope formula

(x1, y1) and (x2,y2) is a known points on the line. We can get these points from the question or give on the point the line intersects.

Since we now now m we can move onto b, the y intercept that’s our intersection of the y-axis in a graph. It’s our initial value.

Sometimes well be asked find b or the y intercept

Ways to Find b/y-intercept:

• Using the point where the line crosses the y-axis, which has the x-coordinate of 0, to directly determine the value of b.

we can replace the x, y and m variables in slope-intercept form if they give us a coordinate and the slope. Remember the slope can any one of them can be negative.

In word problems m and b are often represented by real-world quantities, so we must translate linear equations in order to solve what SAT ask us.

words for m are commonly found to be:

• rate

• each

•  per

• rate of change

• Increasing/Decreasing/Growth

• Daily/Monthly/Yearly

• cost per item

• For each/Per/For every

• incline

• Steepness

Words for b are often found to be:

•  initial

• starting

• one-time

• beginning

• constant. 

Words to refer to these value:

Constant: any term that is a number

Approximate: Means nearly accurate or close to. This indicates that the answer might be an estimation rather than an exact calculation.

The memorization or familiarity of these will be a que when encountering any word problems that you must identify with them.

Often we are not given y = mx + b or a graph to find m and b, the question will give us formula that follow this format.

Standard Form “ax + by = C” or Point Slope form “y1 - y2 = x (x1 + x2)”

Both these formula can be converted into slope intercept form(remember its y=mx +b)

well use that conversion to find the m and b(slope and y-intercept)

Point slope form how to solve and conversion