Other commonly used forms include point-slope form and standard form. Depending on the context that a linear equation is being used in, certain forms can be more beneficial to use. Slope-intercept form is just one of a number of different forms of linear equations, albeit it is the most commonly used form. Thus, the y-intercept occurs at the point (0, 3). For example, given the line 3x + 2y = 6, the y-intercept can be found by plugging 0 in for x, then solving for y. It follows that, given an equation, setting x equal to 0 and solving for y will yield the y-intercept of the line. If a graph is given, the point at which the line intersects the y-axis is the y-intercept. ![]() The y-intercept can be found in a number of ways. Given at least two points on a line, the slope of the line can be found using the slope formula:įor example, given the that (1, 5) and (-2, 7) are points on the same line, the slope of the line can be found as follows: How to find the slope and the y-intercept Once the slope and y-intercept are known, writing the equation of the line just involves plugging the slope and y-intercept into m and b respectively. We found the y-intercept by plugging the given values into the equation y = mx + b, then solving for b. y = mx + bīecause we are given slope and a point on a line, we just need to find the y-intercept in order to write the equation of the line in slope-intercept form. Look Out: when using slope-intercept form to graph lines, always make sure the equation is solved for y so that the equation is in the form y = mx + b.Given m = 3 and the point (3, 5), find b, and write the equation of the line in slope-intercept form. ![]() From there, we "rise" -2, which means we go down 2 units, but we don't put a point there yet. We put a point at 6 on the y-axis since 6 is the y-intercept. Now our equation is in slope-intercept form and we can graph it. What if the equation isn't solved for y already? Well, we'll just have to solve it for y, won't we ?įirst things first: solve for y by subtracting the 2 x term and dividing by 3. Next, since we know that the slope is 2, also known as, we know that another point will be 2 units up and 1 unit over (in the positive direction of course). Our equation is in slope-intercept form, so we know that the number in front of x is the slope (2), and 1 is the y-intercept. What does the graph of y = 2 x + 1 look like? Let's examine how to graph an equation in slope-intercept form. Remember: the slope ( m) is equal to the change in y divided by the change in x, or "rise over run." Slope-intercept form of a line: y = mx + b In the equation y = -9 x, the slope is -9 and the y-intercept is 0, since there's no constant. ![]() Don't let the order of the terms trip you up: we can rearrange it so it looks like y = -8 x + 4. ![]() In the equation y = 4 – 8 x, the slope is -8 (the coefficient of the x-term) and the y-intercept is 4. That means the graph passes through the point (0, 1). The constant is 1, so the y-intercept is 1. The coefficient of the x-term is 2, so the slope is 2. The equation y = 2 x + 1 is in slope-intercept form. If the equation of a line is in slope-intercept form, it looks like this:
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