a Sketch a conceptual graph for both lines, starting with the y-intercepts and then adding the slopes.
B
b Sketch a conceptual graph for both lines, starting with the y-intercepts and then adding the slopes.
A
a Negative
B
b Positive
Practice makes perfect
a The solution of the equation ax+b=cx+d will be the x-coordinate of the point where the lines y=ax+b and y=cx+d intersect. To simplify this solution we will analyze the lines separately. Notice that both of these equations are given in the form
y=mx+b,
where m is the slope of the line and b is the y-intercept. Thus, a and c represent the slopes of the lines while b and d represent the y-intercepts. It is given that
0
Now that we have placed the y-intercepts, we can sketch the lines using the slopes. Since a
From the graph, we can see that the lines intersect at a negative x value. Thus, the solution to
ax+b=cx+d
is negative.
b It is given that
d
Now that we have placed the y-intercepts, we can sketch the lines using the slopes. Since a
From the graph, we can see that the lines intersect at a positive x value. Thus, the solution to
ax+b=cx+d
is positive.
