Writing Equations of Lines All Form

2x + 4y = 10

Write the equation of a line in standard form with a slope (m) of -1/2 and passing through the point (2, 3).

Start with the point-slope form: y - 4 = (-1/3)(x - 6). Then, convert it to standard form: 3(y - 4) = -1(x - 6).

Write the equation of a line in standard form with a slope (m) of -1/3 passing through the point (6, 4).

Start with the point-slope form: y - 5 = (-3/2)(x - 2). Then, convert it to standard form: 2(y - 5) = -3(x - 2).

Write the equation of a line in standard form with a slope (m) of -3/2 passing through the point (2, 5).

5x - y = -20

Write the equation of a line in standard form with a slope (m) of 1/5 and passing through the point (5, 7).

y = -3x + 5

Write the equation of a line with a slope (m) of -3 and a y-intercept (b) of 5 in slope-intercept form.

y - (-5) = (3/4)(x - (-3)), which simplifies to y + 5 = (3/4)(x + 3).

Write the equation of a line with a slope (m) of 3/4 passing through the point (-3, -5) in point-slope form.

x = 3

Write the equation of a vertical line in standard form passing through the point (3, 0).

Vertical lines have undefined slopes, so the equation is x = -3.

Write the equation of a vertical line passing through the point (-3, 5) in standard form.

Vertical lines have undefined slopes, so the equation is x = 4.

Write the equation of a vertical line passing through the point (4, 2) in standard form.

y = -4

Write the equation of a horizontal line in slope-intercept form with a y-coordinate (b) of -4.

Horizontal lines have slopes of 0, so the equation is y - (-5) = 0(x - any x-coordinate), which simplifies to y + 5 = 0.

Write the equation of a horizontal line with a y-coordinate (b) of -5 in point-slope form.

Horizontal lines have slopes of 0, so the equation is y = 2.

Write the equation of a horizontal line with a y-coordinate (b) of 2 in slope-intercept form.

y - 1 = (-4/3)(x + 2)

Write the equation of a line in point-slope form with a slope (m) of -4/3 passing through the point (-2, 1).

y - 5 = 3(x - 4)

Write the equation of a line in point-slope form with a slope (m) of 3 passing through the point (4, 5).

y + 3 = (5/2)(x + 1)

Write the equation of a line in point-slope form with a slope (m) of 5/2 passing through the point (-1, -3).

y = 7

Write the equation of a line in slope-intercept form with a slope (m) of 0 and a y-intercept (b) of 7.

y = x + 2

Write the equation of a line in slope-intercept form with a slope (m) of 1 and a y-intercept (b) of 2.

y = 2x - 3

Write the equation of a line in slope-intercept form with a slope (m) of 2 and a y-intercept (b) of -3.

Since the new line is parallel, it will have the same slope, so the equation is y - (-3) = 2(x - 4), which simplifies to y + 3 = 2(x - 4).

A line is parallel to the line y = 2x + 1 and passes through the point (4, -3). Write the equation of the new line in point-slope form.

Since the new line is parallel, it will have the same slope, so the equation is y = 2x + b. Plug in the point (3, 7) to find the y-intercept, b: 7 = 2(3) + b, b = 1. Therefore, the equation is y = 2x + 1.

A line is parallel to the line y = 2x - 3 and passes through the point (3, 7). Write the equation of the new line in slope-intercept form.

Perpendicular lines have slopes that are negative reciprocals. The slope of the new line is 2. Use the point (2, 6) to find the equation: y - 6 = 2(x - 2).

A line is perpendicular to the line y = -1/2x + 4 and passes through the point (2, 6). Write the equation of the new line in point-slope form.

Perpendicular lines have slopes that are negative reciprocals. The slope of the new line is 1/4. Use the point (-1, 3) to find the equation: 3 = (1/4)(-1) + b, b = 4. Therefore, the equation is y = (1/4)x + 4.

A line is perpendicular to the line y = -4x + 2 and passes through the point (-1, 3). Write the equation of the new line in slope-intercept form.

Use the point-slope form: y - 3 = -2(x - 2), and then simplify to get the slope-intercept form: y = -2x + 7.

A line passes through the point (2, 3) and has a slope (m) of -2. Write the equation of the line in slope-intercept form.

First, find the slope using the formula m = (y₂ - y₁) / (x₂ - x₁). m = (8 - 2) / (3 - (-1)) = 6 / 4 = 1.5. Then, choose one of the points, say (-1, 2), and plug them into the point-slope form: y - 2 = 1.5(x - (-1)), which simplifies to y - 2 = 1.5(x + 1).

A line passes through the points (-1, 2) and (3, 8). Write the equation of the line in point-slope form.

First, find the slope using the formula m = (y₂ - y₁) / (x₂ - x₁). m = (7 - (-3)) / (5 - 1) = 10 / 4 = 2. Then, choose one of the points, say (1, -3), and plug them into the point-slope form: y - (-3) = 2(x - 1).

A line passes through the points (1, -3) and (5, 7). Write the equation of the line in point-slope form.

First, find the slope using the formula m = (y₂ - y₁) / (x₂ - x₁). m = (10 - 4) / (6 - 2) = 6 / 4 = 1. Then, use one of the points and the slope to write the equation: y - 4 = 1(x - 2).

A line passes through the points (2, 4) and (6, 10). Write the equation of the line in slope-intercept form.