How to Draw Graphs
The graph of y = ax + b is a straight line. Starting from the intercept b, draw the straight line using the slope a.
Steps for Drawing a Graph
① Plot the y-intercept (0, b)
② Use the slope a = (increase in y)/(increase in x) to plot one more point
③ Connect the two points and draw a straight line
Example ①
Draw the graph of y = 2x − 3.
Answer: Intercept b=−3 → plot the point (0,−3). Slope a=2 → when x increases by 1, y increases by 2 → plot the point (1,−1). Connect the two points.
Draw the graph of y = 2x − 3.
Answer: Intercept b=−3 → plot the point (0,−3). Slope a=2 → when x increases by 1, y increases by 2 → plot the point (1,−1). Connect the two points.
Example ②
Draw the graph of y = −(2/3)x + 2.
Answer: Intercept (0,2). Slope −2/3 → when x increases by 3, y decreases by 2 → plot the point (3,0). Connect the two points.
Draw the graph of y = −(2/3)x + 2.
Answer: Intercept (0,2). Slope −2/3 → when x increases by 3, y decreases by 2 → plot the point (3,0). Connect the two points.
Key Points
- First, plot the intercept (0,b)
- If the slope a is a fraction, move x by the denominator
- a > 0 → rises from left to right, a < 0 → falls from left to right
Practice Problems
- Find the y-intercept of y = 3x − 1 and the value of y when x=2.
- For y = −x + 4, find the x-intercept (the value of x when y=0).
Answers and Explanations
- Answer: y-intercept −1; when x=2, y=5.
- Answer: x-intercept 4. 0=−x+4 → x=4.