Description of the document: The document is about Straight Line. Determine the Slope of the
line and the Intercept with Steps. Convert General Form to Standard Form and vice versa with Steps;
Converting Slope-Intercept Form to General Form with Steps; Find the Equation of the line given the
Two-Point Slope Form with Graph, Intercept Form with Graph. Find the between the following parallel
lines (Distance from a Line to a Point) with Graph and steps. More example with Formulas and
corresponding step by step process and graphs.
THE STRAIGHT LINE
• The General and Standard Form
Example1. Write the standard equation of the line 4𝑥 + 9𝑦 − 36 = 0 and determine the slope
of the line and the intercept.
4𝑥 + 9𝑦 − 36 = 0 Given in General Form
1 Transpose 4x then multiply both side
(9𝑦 = −4𝑥 + 36) 1
9 by to eliminate the coefficient 9
9
4
𝑦 = −9𝑥 +4 Standard Equation
4
∴ 𝑇ℎ𝑒 𝑠𝑙𝑜𝑝𝑒 𝑚 = 9 𝑎𝑛𝑑 𝑡ℎ𝑒 𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡 𝑖𝑠 (0,4)
5 1
Example2. Represent the standard equation of the line 𝑦 = 6 𝑥 + 5 in general form.
5 1
𝑦 = 6𝑥 + 5 Given in Standard Form
5 1 Equate the given then multiply both
30 (6 𝑥 − 𝑦 + 5 = 0 ) side by 30 to eliminate fractions
25𝑥 − 30𝑦 + 6 = 0 General Form
• Slope-Intercept Form
8
Example3. Write the general form of the line with 𝑚 = 7 and y-intercept of 4.
𝑦 = 𝑚𝑥 + 𝑏 Slope-Intercept Form
Substitute the given then multiply
8
7 (𝑦 = 7 𝑥 + 4) both side by 7 to eliminate fraction
7𝑦 = 8𝑥 + 28 Arrange the given in general form
8𝑥 − 7𝑦 + 28 = 0 General Form
Example4. Find the equation of the line which passes through the point (0,2) and has the
3
slope 𝑚 = 4 .
(𝑦 − 𝑦1 ) = 𝑚(𝑥 − 𝑥1 ) Formula
3 Substitute the
(𝑦 − 2) = (𝑥 − 0) given in the formula
4
3
𝑦 − 2 = 4𝑥 − 0 Simplify
3 Transpose -2 to the other side
𝑦 = 4𝑥 + 2 then simplify similar terms
Equate the equation then multiply
line and the Intercept with Steps. Convert General Form to Standard Form and vice versa with Steps;
Converting Slope-Intercept Form to General Form with Steps; Find the Equation of the line given the
Two-Point Slope Form with Graph, Intercept Form with Graph. Find the between the following parallel
lines (Distance from a Line to a Point) with Graph and steps. More example with Formulas and
corresponding step by step process and graphs.
THE STRAIGHT LINE
• The General and Standard Form
Example1. Write the standard equation of the line 4𝑥 + 9𝑦 − 36 = 0 and determine the slope
of the line and the intercept.
4𝑥 + 9𝑦 − 36 = 0 Given in General Form
1 Transpose 4x then multiply both side
(9𝑦 = −4𝑥 + 36) 1
9 by to eliminate the coefficient 9
9
4
𝑦 = −9𝑥 +4 Standard Equation
4
∴ 𝑇ℎ𝑒 𝑠𝑙𝑜𝑝𝑒 𝑚 = 9 𝑎𝑛𝑑 𝑡ℎ𝑒 𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡 𝑖𝑠 (0,4)
5 1
Example2. Represent the standard equation of the line 𝑦 = 6 𝑥 + 5 in general form.
5 1
𝑦 = 6𝑥 + 5 Given in Standard Form
5 1 Equate the given then multiply both
30 (6 𝑥 − 𝑦 + 5 = 0 ) side by 30 to eliminate fractions
25𝑥 − 30𝑦 + 6 = 0 General Form
• Slope-Intercept Form
8
Example3. Write the general form of the line with 𝑚 = 7 and y-intercept of 4.
𝑦 = 𝑚𝑥 + 𝑏 Slope-Intercept Form
Substitute the given then multiply
8
7 (𝑦 = 7 𝑥 + 4) both side by 7 to eliminate fraction
7𝑦 = 8𝑥 + 28 Arrange the given in general form
8𝑥 − 7𝑦 + 28 = 0 General Form
Example4. Find the equation of the line which passes through the point (0,2) and has the
3
slope 𝑚 = 4 .
(𝑦 − 𝑦1 ) = 𝑚(𝑥 − 𝑥1 ) Formula
3 Substitute the
(𝑦 − 2) = (𝑥 − 0) given in the formula
4
3
𝑦 − 2 = 4𝑥 − 0 Simplify
3 Transpose -2 to the other side
𝑦 = 4𝑥 + 2 then simplify similar terms
Equate the equation then multiply
