2. Graphs of Equations

Use the given conditions to write an equation for each line in point-slope form and slope-intercept form. Slope = −1, passing through (−4, − 1/4)

Find the average rate of change of f(x) = x^2 - 4x from x_1 = 5 to x_2 = 9.

Graph each equation in a rectangular coordinate system. y = -2

Write the point-slope form of the equation of a line that passes through the points $\(\left\)(2,1\(\right\))$ and $\(\left\)(-4,3\(\right\))$ . Then graph the equation.

Write an equation for each line described. Give answers in standard form for Exercises 11–20 and in slope-intercept form (if possible) for Exercises 21–32. through (-1,3), and (3,4)

Find the slope of each line, provided that it has a slope. through (2, -2) and (3, -4)

Graph the line satisfying the given conditions. through (2, -4), m = 3/4

For each line, (a) find the slope and (b) sketch the graph. 5x - 2y = 10

Exercises 143–145 will help you prepare for the material covered in the next section. Solve for y: 3x + 2y − 4 = 0.

For each line, (a) find the slope and (b) sketch the graph. 2y = -3x

Write the point-slope form of the equation of a line with a slope of $0$ that passes through $\(\left\)(2,-4\(\right\))$ . Then graph the equation.

If three distinct points A, B, and C in a plane are such that the slopes of nonvertical line segments AB, AC, and BC are equal, then A, B, and C are collinear. Otherwise, they are not. Use this fact to determine whether the three points given are collinear. (-1, -3), (-5, 12), (1, -11)

Write an equation in slope-intercept form of a linear function f whose graph satisfies the given conditions. The graph of ƒ passes through (−6, 4) and is perpendicular to the line that has an x intercept of 2 and a y-intercept of -4.

Solve each system for x and y, expressing either value in terms of a or b, if necessary. Assume that a ≠ 0 and b ≠ 0. For the linear function f(x) = mx + b, f(−2) = 11 and ƒ(3) = -9. Find m and b.

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I used the ordered pairs (- 2, 2), (0, 0), and (2, 2) to graph a straight line.