Let (x1, y1) = (0, 6) and (x2, y2) = (4, 0), then
slope = m = (y2 - y1)/(x2 - x1)
m = (0 - 6)/(4 - 0) = -6/4 = -3/2
Thus, the slope of a line that passes though points (0, 6) and (4, 0) is -3/2.
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If you mean: 4x+5y = 40 then y = -0.8x+8 whereas as -0.8 is the slope and 8 is the y intercept of a straight line equation
5x+8y = 40 8y = -5x+40 y = -5/8x+5 in slope intercept form
Oh, dude, you just gotta rearrange that equation a bit. So, like, first divide by 5 to get -4x - y = 8. Then, if you wanna be all fancy and use slope-intercept form, just solve for y to get y = -4x + 8. And there you have it, a technically correct answer with a sprinkle of my signature humor.
In regards to roofs. "Pitch" is a ratio of the total rise of a roof over the total span of a building. "Slope" is a ratio of the total rise of a roof over "half" the total span of a building. A building 40 feet wide with a total roof rise of 10 feet (from the top of the supporting walls) has a pitch of 10/40 reduced to 1:4 A building of the same dimensions will have a slope of 1:2 or 6/12 on the imperial framing square.
First we need to find the equation of the tangent line to the parabola at (2, 20).Step 1. Take the derivative of the function of the parabola.Let f(x) = 5x^2f'(x) = 10xStep 2. Find the slope of the tangent line at x = 2. Evaluate f'(2).f'(2) = 2 x 10 = 20Step 3. Using the slope, m = 20, and the point (2, 20), find the equation of the tangent line at that point. Use the point-slope form of a line(y - y1) = m(x - x1)(y - 20) = 20(x - 2)y - 20 = 20x - 40 add 20 to both sidesy = 20x - 20Step 4. Find the points of intersections of y = 5x^2 and y = 20x - 205x^2 = 20x - 20 Divide by 5 to both sidesx^2 = 4x - 4 subtract 4x and add 4 to both sidesx^2 - 4x + 4 = 0 factor(x - 2)^2= 0x = 2Step 5. Find the intersection of the tangent line with x-axis.y = 20x - 20y = 020x - 20 = 0x = 1Since the vertex of the parabola is (0, 0) and the intersection of the tangent line with parabola is (2,20) we use the interval [0, 2] to fin the required area.Step 6. IntegrateA = ∫ [(5x^2)] dx, where the below boundary is 0, and the upper boundary is 2 minus A= ∫ (20x + 20)] dx from 1 to 2= 10/3