Straight Lines

Answer

Step 1: Use the slope formula m = (y₂ - y₁)/(x₂ - x₁) Step 2: Identify coordinates: (x₁, y₁) = (2, 3), (x₂, y₂) = (5, 7) Step 3: Substitute values: m = (7 - 3)/(5 - 2) = 4/3 Step 4: Therefore, slope =

Answer

Step 1: Use slope-intercept form y = mx + c Step 2: Given m = 3, c = -2 Step 3: Substitute: y = 3x + (-2) Step 4: Final equation: y = 3x - 2 This is the SLOPE-INTERCEPT FORM, where: - m = slope of th

Answer

Step 1: Use point-slope form: y - y₁ = m(x - x₁) Step 2: Given point (x₁, y₁) = (4, -1), slope m = 2/3 Step 3: Substitute: y - (-1) = (2/3)(x - 4) Step 4: Simplify: y + 1 = (2/3)x - 8/3 Step 5: Final

Answer

Step 1: Use two-point form: (y - y₁)/(y₂ - y₁) = (x - x₁)/(x₂ - x₁) Step 2: Points: (x₁, y₁) = (-2, 5), (x₂, y₂) = (3, -1) Step 3: Substitute: (y - 5)/(-1 - 5) = (x - (-2))/(3 - (-2)) Step 4: Simplify

Answer

Step 1: Use intercept form: x/a + y/b = 1 Step 2: Given a = 4 (x-intercept), b = -3 (y-intercept) Step 3: Substitute: x/4 + y/(-3) = 1 Step 4: Final equation: x/4 - y/3 = 1 Standard form: 3x - 4y = 1

Answer

Step 1: Start with 3x - 4y + 12 = 0 Step 2: Isolate y: -4y = -3x - 12 Step 3: Divide by -4: y = (3/4)x + 3 Step 4: Compare with y = mx + c Results: - Slope (m) = 3/4 - Y-intercept (c) = 3 General Me

Answer

Step 1: Use distance formula: d = |Ax₁ + By₁ + C|/√(A² + B²) Step 2: From 4x + 3y - 5 = 0: A = 4, B = 3, C = -5 Step 3: Point (x₁, y₁) = (2, -3) Step 4: Substitute: d = |4(2) + 3(-3) + (-5)|/√(4² + 3²

Answer

Step 1: Identify slopes: m₁ = 2, m₂ = -1/3 Step 2: Use angle formula: tan θ = |m₁ - m₂|/|1 + m₁m₂| Step 3: Calculate: tan θ = |2 - (-1/3)|/|1 + 2(-1/3)| Step 4: Simplify: tan θ = |2 + 1/3|/|1 - 2/3| =