Consider this: you are starting off with two equations, y = x^2 – kx and y = 4x – 9, but there are three unknowns; x, y, and k. By finding the derivative, we can create a third equation. Set the derivative equal to the slope of the line:

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Nov 22, 2017 · 6 a Find the coordinates of the vertex of the parabola y = 4x 2 − 12 x + 7. [4] b Find the values of the constant k for which the line y = kx + 3 is a tangent to the curve y = 4x 2 − 12 x + 7. [3] EXERCISE 50 1 The graph of y = 6x-x2 is shown below. y 5 The marked point, P, is (1, 5). (i) Find the gradient function Z. (iil Find the gradient of the curve at P. (iiil Find the equation of the tangent at P. 2 lil Sketch the curve y= 4x-x2• lil Differentiate y = 4x-x2. (iiil Find the gradient of y = 4x-x2 at the point ( 1, 3). X Dec 30, 2020 · Re: The graph below of a line in the standard (x,y) coordinate plane corre Wed Dec 30, 2020 12:38 am Equation of the line is, y=mx+c where m is the slope and c is the y intercept 18. Lee thinks ofa line represented by the equationy —4x ± 6. Which line on the graph below is •steeper than Lee’s line and • has ay-interceptthat has halfthe value of Lee’s line? ap bq 19. A line has ay-interceptof4 and a slope of—3, Which equation represents this line? a y4x±3 b y4x—3 c y4±3x (y43x • I)-2---6

Again, we draw a number line with the critical point 3/4 labeled. We use test points to determine the sign of the second derivative. y'(0) = -56(4(0) - 3)-3 = -56/27 > 0 y'(1) = -56(4(1) - 3)-3 = 56 < 0. We conclude that the graph is concave up on (-, 3/4) and concave down on (3/4, ). E) We use the above information to graph the function. (c) Draw a table of values and the graph of the linear equation y = 2x. Answer: (a) Gradient = 2 (b) y-intercept = 0 (c) Because this graph is a straight line, only 3 points are needed - two points for drawing the line, and the third for checking correctness. Choose x = 0, 1, 2 unless the question states otherwise. y=4x-5 Geometric figure: Straight Line Slope = 8.000/2.000 = 4.000 x-intercept = 5/4 = 1.25000 y-intercept = -5/1 = -5.00000 Rearrange: Rearrange the equation by subtracting what is ...Gradients of Straight Line Graphs. Equations featuring x and y (and no x^3 or y^2 etc.) are straight lines.. The gradient of a line is a measure of how steep it is. If the gradient is small, the slope of the line will be very gradual, but if the gradient is big, the line will be quite steep.

3-97. Graph the lines y = −4x + 3 and y = x − 7 on the same set of axes. Then find their point of intersection. General Form for the Equation of a Line Ax + By = C , where A > 0 and, if possible, A , B , and C are relatively prime integers . The standard form is used in some algebra classes for practice in manipulating equations . a) y = x + 12 b) y = 7x – 42 c) y = 4x – 16 d) y = -2x - 45 2) Solve for y if x = 5: a) y = x + 13 b) y = 6x – 32 c) y = 2x – 15 d) y = 8x - 5 3) Graph each coordinate pair on the graph and then indicate which quadrant or axis the point lies on. Plot the solution points you have found for equation 2, and note that all the points lie on a line. That line is the graph of equation 2. The most straight forward technique for graphing equations is to plot solution points until a geometric pattern emerges. Equation 3: y = 4x - x 2 - 2. Exercise 4: MAT Practice test and model papers are also available. Use youth4work free online platform for preparing MAT exam topic of Data Analysis and Sufficiency, this Data analysis/suffic