2(x1,y1) (x2,y2) Slope Problem Examples Determine a value for x such that the line through the points has the given slope.(x1,y1)(x2,y2)Let's use the slope formula and plug in what we know.You can cross-multiply to find a fraction-free equation for x to solve.
3(0,-3) (1,-1) (-1,5) Example when you have a point and the slope A point on a line and the slope of the line are given. Find two additional points on the line.+1+2To find another point on the line, repeat this process with your new point-1Remember that slope is the change in y over the change in x. The slope is 2 which can be made into the fraction(0,-3)(0,-3)+1+2So this point is on the line also. You can see that this point is changing (adding) 2 to the y value of the given point and changing (adding) 1 to the x value.(1,-1)(-1,5)
4Example of given an equation, find the slope and y intercept Find the slope and y intercept of the given equation and graph it.First let's get this in slope-intercept form by solving for y.-3x-3x +4Now plot the y intercept-4-4Change in yChange in xy interceptslopeFrom the y intercept, count the slopeNow that you have 2 points you can draw the line
5Example of how to find x and y intercepts to graph a line The x-intercept is where a line crosses the x axisWhat is the common thing you notice about the x-intercepts of these lines?(-1,0)(2,0)(6,0)The y value of the point where they cross the axis will always be 0To find the x-intercept when we have an equation then, we will want the y value to be zero.
6Now let's see how to find the y-intercept The y-intercept is where a line crosses the y axis(0,5)(0,4)What is the common thing you notice about the y-intercepts of these lines?(0,1)The x value of the point where they cross the axis will always be 0To find the y-intercept when we have an equation then, we will want the x value to be zero.
7Find the x-intercept. Let's look at the equation 2x – 3y = 12 We'll do this by plugging 0 in for y2x – 3(0) = 12Now solve for x.2x = 12So the place where this line crosses the x axis is (6, 0)x = 6
8Find the y-intercept. 2x – 3y = 12 We'll do this by plugging 0 in for x2(0) – 3y = 12Now solve for y.-3y = 12So the place where this line crosses the y axis is (0, -4)y = - 4(6,0)We now have enough information to graph the line by joining up these points(0,- 4)