Solving Slope Problems

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You have probably heard how to find a slope by finding the "rise over run." This means exactly the same thing--change in $y$ over change in $x$.

$$/$$ Let's look at an example: Say we are given this graph and asked to find the slope of the line. To do this, we must first mark points along the line to in order to compare them to one another. $x = 3$ $y = 3$ The steeper the line, the larger the slope.

In order to find the slope of the line, we can simply trace our points to one another and count. This means our slope is: $-$ A slope can either be positive or negative. Now, we already know how to count to find our slope, so let us use our equation this time.

We've highlighted in red the path from one coordinate point to the next. $/$ Let us assign the coordinate (-1, 0) as $(x_1, y_1)$ and (1, 3) as $(x_2, y_2)$.

For example, if a two lines are perpendicular to one another and one has a slope of 4 (in other words, $4/1$), the other line will have a slope of $-$. $8x 9y = 3$ $9y = -8x 3$ $y = - 1/3$ Now, we can identify our slope as $-$.

Two lines that will never meet (no matter how infinitely long they extend) are said to be parallel. We also know that parallel lines have identical slopes.This is to test you on how well you're paying attention and get people who are going too quickly through the test to make a mistake. Now, let’s use both sets of coordinates—$(2, 6)$ and $(0, 8)$—to find the slope of the line: $/$ $(8 - 6)/(0 - 2)$ $-$ $-1$ So the slope of the line is -1. (Note: don’t let yourself get tricked into trying to find $A$!For some real number A, the graph of the line $y=(A 1)x 8$ in the standard $(x,y)$ coordinate plane passes through $(2,6)$. It can become instinct when working through a standardized test to try to find the variables, but this question only asked for the . 8 First, let us re-write our equation into proper slope-intercept equation form.So when we put that together, we can find the equation of our line at: $y = mx b$ $y = x 3$ Remember: always re-write any line equations you are given into this form! The $b$ in the equation is the y-intercept (in other words, the point at the graph where the line hits the y-axis at $x = 0$).The test will often try to trip you up by presenting you with a line NOT in proper form and then ask you for the slope or y-intercept. This means that, for the above equation, we also have a set of coordinates at $(0, 8)$.This time, coordinates (-1, 0) will be our $(x_2, y_2)$ and coordinates (1, 3) will be our $(x_1, y_1)$.$/$ $(0 - 3)/(-1 - 1)$ $/$ /2$ As you can see, we get the answer /2$ as the slope of our line either way.This means that they are continuously equidistant from one another. You can see why this makes sense, since the rise over run will always have to be the same in order to ensure that the lines will never touch. So all lines parallel to this one will have the slope of $-$. Most line and slope questions on the ACT are quite basic at their core. $-$ We have two sets of coordinates, which is all we need in order to find the slope of the line which connects them.What is the slope of any line parallel to the line x 9y=3$ in the standard $(x,y)$ coordinate plane? You’ll generally see two to three questions on slopes per test and almost all of them will simply ask you to find the slope of a line when given coordinate points or intercepts. So let us plug these coordinates into our slope equation: $/$ $(7 - 2)/(6 - -5)$ /11$ Our final answer is J, /11$ Despite the fact that we are now working with figures, the principle behind the problem remains the same--we are given a set of coordinate points and we must find their slope.If you’ve gone through the guide on coordinate geometry, then you know that coordinate geometry takes place in the space where the $x$-axis and the $y$-axis meet.Any point on this space is given a coordinate point, written as $(x, y)$, that indicates exactly where the point is along each axis.


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