Summary
Highlights
Learn how to calculate the slope of a line passing through two given points using the formula (y2 - y1) / (x2 - x1). An example calculates the slope between (2, -3) and (4, 5) as 4.
Understand how to identify the slope (m) and y-intercept (b) from a linear equation in slope-intercept form (y = mx + b). For the equation y = 2x - 3, the slope is 2 and the y-intercept is -3 (or (0, -3)).
Discover how to graph equations where x equals a constant (resulting in a vertical line) and y equals a constant (resulting in a horizontal line). Examples graph x = 2 and y = 3.
Learn to graph a linear equation by using its slope and y-intercept. The y-intercept provides the starting point, and the slope (rise over run) helps locate subsequent points to draw the line. An example graphs y = 3x - 2.
Find out how to graph a linear equation by calculating its x and y-intercepts. By setting y to 0 to find the x-intercept and x to 0 to find the y-intercept, you can easily plot two points and draw the line. An example graphs 2x - 3y = 6.
Practice writing the equation of a line given a point and a slope. The point-slope formula (y - y1 = m(x - x1)) is introduced, and then the equation is converted into slope-intercept form. An example uses point (2, 5) and slope 3.
Learn how to write the equation of a line when given two points. First, calculate the slope using the two points, then use the point-slope formula with one of the points and the calculated slope. An example uses points (-3, 1) and (2, -4).
Understand that parallel lines have the same slope. To write the equation of a line parallel to another, first find the slope of the given line, then use that slope with the given point in the point-slope formula. An example finds the equation for a line parallel to 2x + 5y - 3 = 0, passing through (3, -2).
Learn about perpendicular lines, which have slopes that are negative reciprocals of each other. The process involves finding the slope of the given line, determining its negative reciprocal, and then using the given point with this new slope in the point-slope formula. An example finds the equation for a line perpendicular to 3x - 4y + 5 = 0, passing through (-4, -3).