Final answer:
To sketch two intersecting lines, you can use two linear equations with different slopes and y-intercepts. For example, one can be y = 3x + 9 and another y = -2x + 5. Sketch them on a graph with x and y axes, and the point where they cross is the intersection.
Step-by-step explanation:
To sketch two intersecting lines, with one represented by IJ and the other by xYʸᴛʰ, we begin by understanding that lines on a graph can be described by linear equations. For instance, in Figure A1 Slope and the Algebra of Straight Lines, we see a line graph with x on the horizontal axis and y on the vertical axis.
The line graph has a specific y-intercept and a constant slope throughout its length. The slope, denoted as m, shows a rise of 3 units in the y-direction for every one unit increase along the x-axis. This is expressed mathematically as m = 3. The y-intercept, denoted as b, is the point where the line crosses the y-axis, and in this case, it is 9.
Based on this, the equation of the line is y = 3x + 9. To sketch two intersecting lines, we can choose two different slopes and y-intercepts for each line. For example, you can sketch one line as y = 3x + 9, and another line could be y = -2x + 5. The different slopes ensure that the lines intersect, and the y-intercepts give us the starting points to draw the lines on the y-axis.