☰ Year plan · Mathematics

The equation of a straight line

Week 13 · The equation of a straight line: slope and y-intercept, point and slope, two points, standard form and applications · 3 lessons
1

The equation y = mx + b: slope and y-intercept, and drawing the line

Mathematics Prep 3 Term 1, Unit 3, Lesson 7
GoalRead the slope and y-intercept from y = mx + b, write the equation, and draw the line.
New words
y-intercept · the number b: where the line cuts the y-axis, the point (0, b)slope-intercept form · the equation y = mx + bfixed charge · a starting amount, not depending on how much we userate · how much y changes when x increases by 1
Explanation

A line with slope m that cuts the y-axis at (0, b) has the equation y = mx + b. In y = 2x + 3 the slope is 2 and the y-intercept is 3. To draw it: plot (0, 3); from there go 1 to the right and m = 2 up, reaching (1, 5); then draw the line through the points. If the slope is a fraction such as −1/2, go 2 to the right and 1 down. Going back: slope 3 and y-intercept −2 give y = 3x − 2. In stories, m is the rate and b the starting amount: a taxi costs 5 LE to start plus 2 LE for each km, so the cost is y = 2x + 5. For 8 km: y = 2 × 8 + 5 = 21 LE.

xy−3−2−112345−3−2−11234567890y = 2x + 3(0, 3)(1, 5)
Worked examples
Find the slope and y-intercept of y = −x/2 + 1. Slope m = −1/2 and y-intercept b = 1. The line passes (0, 1) and, after 2 right and 1 down, (2, 0).
Write the equation of the line with slope 3 and y-intercept −2: y = 3x − 2.
A plumber charges 40 LE to visit plus 15 LE per hour. Write the cost y after x hours and find it for 3 hours. y = 15x + 40, and 15 × 3 + 40 = 85 LE.
Class activity

Phone plan. A plan costs 30 LE per month plus 0.5 LE per minute. Draw the cost line for 0 to 60 minutes on squared paper. What does 30 represent?

Practice
1
State the slope and y-intercept of y = 5x − 4.
2
Write the line with slope −2 through (0, 6).
3
Write y = 4 − 3x in the form y = mx + b and give its slope.
4
A gym costs 100 LE joining fee plus 60 LE per month. Write the total y after x months and find it for 6 months.
5
Draw y = −x + 2 using its slope and y-intercept.