Page 21 - Algebra

REMEMBER:
𝐶h𝑎𝑛𝑔𝑒 𝑖𝑛 𝑦
•
• Slope or m of line passing through
• To calculate the x-intercept, put y = 0, and solve for x.
• To calculate the y-intercept, put x = 0, and solve for y.
Rate of change =
𝐶h𝑎𝑛𝑔𝑒 𝑖𝑛 𝑥
(x1, y1) and (x2, y2) = 𝑦2− 𝑦1 𝑥2− 𝑥1
2.6. Point-slope Form of an Equation
The slope-intercept form of a linear equation is given by: y = mx + b where m = slope
b = y-intercept
The point-slope form of an equation is given by
y – y1 = m(x – x1), where (x1, y1) is a point lying on the line, and m is the slope.
REMEMBER:
• The point-slope form of an equation is given by
y – y1 = m(x – x1), where (x1, y1) is a point lying on the line, and m is the slope.
• To find the linear equation, using the point-slope form of an equation passing through (x1, y1) and (x2, y2), follow these steps:
Step 1: Find the value of the slope ‘m’.
Step 2: Put the value of x1 and y1 in y – y1 = m(x – x1) Step 3: Solve to get the equation.
Worked Example
Find the equation of a line passing through (4, 3) and (
Solution:
m = 𝑦2− 𝑦1 𝑥2− 𝑥1
y1 = 3 y2 =
–2, –9).
–9
y–y1 =m(x–x1)
x1 = 4 x2 = – 2
Put m in
𝑦2− 𝑦1 −9−3 −12
m= = ===2
𝑥2− 𝑥1 −2−4 −6
y – 3 = 2(x – 4)
y – 3 = 2x – 8
y = 2x – 5
Page 20 of 177
Algebra I & II