While the SAT math section includes a handful of useful formulas, all of these âfreebiesâ are directly related to geometry. Â There remain a significant number of important equations that youâll need to know on your own to successfully navigate the math section of the test. Â In this blog post, weâll be looking at what equations youâll need to know about graphing lines.
Equation of a Line: y = mx + b
While youâve no doubt heard this equation for years, if itâs been awhile since youâve last used it, itâs worth a quick review before the big test day. Â Remember:
m = slope of the line
b = the y-intercept for the line (the place on the y-axis where the line youâre graphing hits it)
Note that when the line runs through the origin (0, 0), then the origin is the y-intercept and your equation will look more like y = mx.
If you encounter an equation for a line that isnât in this format, rearrange it until it is. Â The SAT loves to check your familiarity with this equation by asking seemingly simple questions (whether the slope is positive or negative, whatâs the y intercept, etc.) but coupled with an equation thatâs been rearranged just enough to make things tricky, such as b = mx – y. Â By quickly putting it into y = mx + b format, youâll be able to identify useful information about the line without actually graphing it.
Slope formula
Of course, sometimes instead of being given an equation for a line, youâll be provided two points and expected to come up with the equation yourself. Â To do this youâll first need to find the slope.
Remember, slope is equal to the vertical change over the horizontal change. Â If youâve been given two points on the line,
A(x1,y1)
B(x2,y2)
then the formula for finding the slope is:
(y2 – y1)
(x2 – x1)
Once you have the slope, solve your line equation y = mx + b for b using one of the provided coordinates.
Midpoint and Length
Sometimes an SAT question will want to know the midpoint of a line connecting two points. Â If our two points are once again:
A(x1,y1)
B(x2,y2)
then the midpoint is found using this formula:
((x2 + Â x1), (y2 + Â y1))
   2             2
Rather than memorizing this equation, though, it may be easier to think of it as taking the average of the two values for x and the average for the two values of y to generate values for the midpoint.
Similarly, sometimes you may also be asked the distance between two points. Â Rather than memorizing the equation
distance = sqrt((x2âx1)^2+(y2ây1)^2)
instead, focus on thinking about the two coordinates as vertices of a right triangle connected by the hypotenuse. Â (You may even want to actually graph it that way to help you visualize it during the test.) Â You can then find the distance between them using the pythagorean theorem, which happens to be one of the included equations on the exam. Â
You can expect to encounter at least a couple of questions related to lines on every SAT exam. Â Since the formulas for working with lines arenât provided, itâs important to take some time beforehand to review the basics to make sure you have things all lined up before the big day.