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Comparing Slopes and Intercepts
Graph showing parallel lines.
Click to zoom
Lines with the same slope (a) but different y-intercepts (b) remain parallel.
Understand the roles of 'a' (slope) and 'b' (y-intercept) in the linear equation y = ax + b, and define parallel lines.
Define slope based on y = ax.
In the linear relationship equation , the letter a represents the slope of the line. The slope tells us how steep the straight line is on a coordinate graph.
Define y-intercept.
In the equation , the constant b is called the y-intercept. This value tells us exactly the distance from the origin where the line cuts the y-axis.
Graph showing parallel lines.
Lines with the same slope (a) but different y-intercepts (b) remain parallel.
Summarize the conditions for parallel lines.
What happens if we keep the slope fixed, but change the value of ? The lines shift up or down the coordinate plane but remain perfectly aligned with the original line.
Worked example based on End of Chapter Q7.
Problem. Find the slope and the y-intercept of the equation .
Faded practice for slope and intercept.
Let us analyze the linear equation given by . To find the slope and y-intercept, we must first express it in the standard form . Dividing the entire equation by , we obtain .
In this form, the coefficient of represents the slope, which is . The constant term represents the y-intercept, which is .
Based on this y-intercept, we can conclude that the line cuts the y-axis at the coordinate point (0, ).