Example Problems with Slope

 

    The Math IC test often asks questions that require you to understand the slope-intercept form and the point-slope form, and to be able to convert between the two.

Here are some practice questions:

    To answer this question, you first need to find the slope of the line whose equation you are trying to determine. Fortunately, the question gives you the slope of a perpendicular line, and we know that the slope of a line is the opposite reciprocal of the slope of the line to which it is perpendicular. Thus, the slope is –1⁄ (¹⁄₃) = –3. If the line contains the point (3, 4), its point-slope equation is y – 4 = –3(x – 3). To convert this to slope-intercept form, use algebra:

    Here’s another question:

    Start by finding the slope of the line. You can calculate the slope with the two points you’re given: m = ^8–3⁄_–1–5 = –⁵⁄₆. To put the equation of this line in slope-intercept form, the only additional we need is the y-intercept. To find it, use the x- and y-coordinates of a point that you know is on the line and plug them into the equation y = –⁵⁄₆ x + b, and solve for b. Using the point (5, 3):

    The slope-intercept form of the equation of this line is y = –⁵⁄₆ x + ⁴³⁄₆.