1.1 TRIG slope and lines review both days

Answer explanation

To find the slope, use the formula: slope = (y2 - y1) / (x2 - x1). Substituting the points (2, 3) and (5, 7), slope = (7 - 3) / (5 - 2) = 4 / 3 = 1.33. Therefore, the correct slope is 3/4.

Answer explanation

To find the slope, use the formula: slope = (y2 - y1) / (x2 - x1). Substituting the given points, slope = (-2 - 4) / (3 - (-1)) = -6 / 4 = -1.5. Therefore, the slope is -1.5.

Answer explanation

The equation of a line with slope 2 passing through the point (1, -3) can be found using the point-slope form: y - y1 = m(x - x1). Substituting the values, we get y - (-3) = 2(x - 1), which simplifies to y = 2x - 5. Therefore, the correct answer is y = 2x - 5.

Answer explanation

The equation of the line passing through two points (0, 0) and (4, 8) can be found using the formula y = mx. By substituting the values of the points, we get m = 8/4 = 2. Therefore, the equation is y = 2x.

Answer explanation

The line y = 2x - 1 is perpendicular to y = -\frac{1}{2}x + 3 because the slopes of perpendicular lines are negative reciprocals. The slope of y = 2x - 1 is 2, the negative reciprocal of -\frac{1}{2}.

Answer explanation

The equation of a line with slope -3/4 passing through (0, 2) is y = mx + b. Substituting m=-3/4 and the point (0, 2) gives y = -3/4x + 2.

Answer explanation

To find the equation of the line passing through two points, first calculate the slope using the formula (y2 - y1) / (x2 - x1). Then substitute one of the points and the slope into the point-slope form y - y1 = m(x - x1) to get the equation y = 2x - 1.

Answer explanation

The line y = -1/5x + 1 is perpendicular because the slope is the negative reciprocal of 5x, which is -1/5.

Answer explanation

To find the slope, use the formula: slope = (y2 - y1) / (x2 - x1). Substituting the given points, slope = (-6 - 2) / (3 - 7) = -8 / -4 = 2. Therefore, the slope is 2.

Answer explanation

The equation of a line with slope 1 passing through (-2, 4) is found using the point-slope form: y - y1 = m(x - x1). Substituting (-2, 4) and m = 1 gives y - 4 = 1(x + 2), which simplifies to y = x + 6. Therefore, the correct answer is y = x + 6.