FIND THE EQUATION OF THE THAT PASSES THROUGH 1. (1,6) (5,1) m = -5/42. (-4, -5) (2, 1)
Answer (1)
Answer:Here's how to find the equations of the lines: 1. (1,6) (5,1) m = -5/4 - Using point-slope form:The point-slope form of a linear equation is: y - y₁ = m(x - x₁)Where (x₁, y₁) is a point on the line and m is the slope. We can use either point (1, 6) or (5, 1) and the given slope: - Using (1, 6): y - 6 = (-5/4)(x - 1)- Using (5, 1): y - 1 = (-5/4)(x - 5) Both of these equations are correct. You can simplify either one to slope-intercept form (y = mx + b) if you prefer.- Simplifying to slope-intercept form:Let's use the equation y - 6 = (-5/4)(x - 1)Distribute: y - 6 = (-5/4)x + 5/4Add 6 to both sides: y = (-5/4)x + 29/4 Therefore, the equation of the line is y = (-5/4)x + 29/4. 2. (-4, -5) (2, 1) - First find the slope:The slope formula is: m = (y₂ - y₁) / (x₂ - x₁) Let (-4, -5) be (x₁, y₁) and (2, 1) be (x₂, y₂) m = (1 - (-5)) / (2 - (-4)) = 6 / 6 = 1 So the slope of the line is 1.- Using point-slope form:We can use either point (-4, -5) or (2, 1) and the slope we just calculated: - Using (-4, -5): y - (-5) = 1(x - (-4))- Using (2, 1): y - 1 = 1(x - 2)- Simplifying to slope-intercept form:Let's use the equation y - (-5) = 1(x - (-4))Simplify: y + 5 = x + 4Subtract 5 from both sides: y = x - 1 Therefore, the equation of the line is y = x - 1.
