Writing the Equation of a Line
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Example | ||
Problem | Write the equation of the line that has a slope of and a y-intercept of −5. | |
Substitute the slope (m) into y = mx + b. | ||
Answer | or | Substitute the y-intercept (b) into the equation. |
What is the equation of a line that has a slope of −2 and goes through the point (0, 8)? A) y = −2x + 8 B) y = 8x – 2 C) y = −2x + 0 D) 0 = 8x – 2 |
Example | ||
Problem | Write the equation of the line that has a slope of 3 and contains the point (1, 4). | |
y = 3x + b | Substitute the slope (m) into y = mx + b. | |
Rapidweaver 8 2 1. 4 = 3(1) + b | Substitute the point (1, 4) for x and y. | |
4 = 3 + b 1 = b | Solve for b. | |
Answer | y = 3x + 1 | Rewrite y = mx + b with m = 3 and b = 1. |
Advanced Example | ||
Problem | Write the equation of the line that has a slope of and contains the point . | |
Substitute the slope (m) into . | ||
Substitute the point for x and y. | ||
Solve for b. | ||
Answer | Rewrite with and . |
Write the slope-intercept form of the line with a slope of and which contains the point (9, 4). A) B) C) D) |
Advanced Question Write the slope-intercept form of the line with a slope of -0.6 and which contains the point (3.8, 7.25). A) y = -0.6x + 3.8 B) y = -0.6x + 4.97 C) y = 3.8x + 7.25 D) y = -0.6x + 9.53 |
Example | ||
Problem | Write the equation of the line that passes through the points (2, 1) and (−1, −5). | |
Find the slope using the given points. | ||
y = 2x + b | Substitute the slope (m) into y = mx + b. | |
1 = 2(2) + b | Substitute the coordinates of either point for x and y– this example uses (2, 1). | |
1 = 4 + b −3 = b | Solve for b. | |
Answer | y = 2x + (−3), or y = 2x – 3 | Rewrite y = mx + b with m = 2 and b = −3. |
y = 2x + b |
−5 = 2(−1) + b |
−5 = −2 + b |
−3 = b |
Advanced Example | ||
Problem | Sqlpro for sqlite 2019 07 08 06. Write the equation of the line that passes through the points (-4.6,6.45) and (1.15,7.6). | |
Find the slope using the given points. | ||
Substitute the slope (m) into . | ||
Substitute either point for x and y– this example uses (1.15,7.6). Then solve for b. | ||
Rewrite with m = 0.2and b = 7.37. | ||
Answer | The equation of the line that passes through the points (-4.6,6.45) and (1.15,7.6) is . |
Write the slope-intercept form of the line that passes through (5, 2) and (−1, −10). A) B) C) D) |
Advanced Question Which of the following lines goes through the points and ? A) B) C) D) |
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