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Line Equation from Two Points

Learn how to write the equation of a line given two points. Includes examples and practice problems.

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Line Equation from Two Points

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  1. EXAMPLE 3 Write an equation of a line given two points Write an equation of the line shown.

  2. y2 – y1 –1 – (–5) 4 m = = = x2 – x1 3 – 0 3 Substitute for mand 5 for b. 4 4 y = x – 5 3 3 EXAMPLE 3 Write an equation of a line given two points SOLUTION STEP 1 Calculate the slope. STEP 2 Write an equation of the line. The line crosses the y-axis at (0, –5). So, the y-intercept is –5. y =mx +b Write slope-intercept form.

  3. y2 – y1 17 – 5 12 m 3 = = = = x2 – x1 4 – 0 4 Write a linear function EXAMPLE 4 Write an equation for the linear function fwith the values f(0) = 5 andf(4) = 17. SOLUTION STEP 1 Write f(0) = 5 as (0, 5) and f (4)= 17 as (4, 17). STEP 2 Calculate the slope of the line that passes through (0, 5) and (4, 17).

  4. ANSWER The function is f(x) = 3x + 5. Write a linear function EXAMPLE 4 STEP 3 Write an equation of the line. The line crosses the y-axis at (0, 5). So, the y-intercept is 5. y =mx + b Write slope-intercept form. y =3x + 5 Substitute 3 for mand 5 for b.

  5. 1 x + 1 – y = ANSWER 2 GUIDED PRACTICE for Examples 3 and 4 3. Write an equation of the line shown.

  6. 4. Write an equation for the linear functionf with the given values. ANSWER 3 y =x – 2 4 GUIDED PRACTICE for Examples 3 and 4 f(0) = –2, f(8) = 4

  7. Write an equation for the linear function fwith the given values. 5. – ANSWER y =x + 5 1 3 GUIDED PRACTICE for Examples 3 and 4 f(–3) = 6, f(0) = 5

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