Solving Slope Problems

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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 $(x_2, y_2)$.

As you go through your line and slope problems, keep in mind these tips: #1: Always rearrange your equation into $y = mx b$ If you are given an equation of a line on the test, it will often be in form (for example: $10y 15x = 20$). If you use this criteria to count along the graph, you will find that you hit no marked points by counting up 2 and over 3 to the left, but you hit D when you go down 2 and over 3 to the right. Method 2—Algebra Alternatively, you can always use your slope formula to find the missing coordinate points.

If you are going too quickly through the test or if you forget to rearrange the given equation into proper slope-intercept form, you will misidentify the slope and/or the y-intercept of the line. If we start with our coordinate points of $(2, 5)$ and our slope of $-$, we can find our next two coordinate points by counting finding the changes in our $x$ and $y$.

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.

The Equation of a Line $$y = mx b$$ This is called the “equation of a line,” also known as an line written in "slope-intercept form." It tells us exactly how a line is positioned along the x and y axis as well as how steep it is.

This is the most important formula you’ll need when it comes to lines and slopes, so let’s break it into its individual parts.

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 $(0, 8)$.


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