Equations of Lines LF.2.AC.7: Write an equation given two points, a point and y-intercept, a point and slope.

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Equations of Lines LF.2.AC.7: Write an equation given two points, a point and y-intercept, a point and slope.

FHSEquations of Lines2 The Forms of Linear Equations The equation of a line can be written in different forms. The slope-intercept form is y = mx + b, where m is the slope and b is the y - intercept. The point-slope form is y – y 1 = m(x – x 1 ), where m is the slope and ( x 1, y 1 ) is a point on the line.

FHSEquations of Lines3 Point-Slope Form Given a point and slope, to write the equation for that line in the point slope form, just put those numbers into the point-slope form and you are done. For example if m = 5 and the point is (2, -3), then the equation would be: y + 3 = 5(x – 2)

FHSEquations of Lines4 Slope Intercept Form Given a slope and a point, to get an equation in slope intercept form, start with the point-slope form, and use Algebra to solve for y. Given two points, first find the slope, then use either one of the points with the slope to write the equation in point-slope form. Then use Algebra to solve for y.

FHSEquations of Lines5 Example: Point and Slope Find the equation of the line if the slope is ¾ and one point on the line is (8, 7). (y – y 1 ) = m(x – x 1 ) (y – 7) = ¾(x – 8) y – 7 = ¾ x – = + 7 y = ¾ x + 1

FHSEquations of Lines6 Example: Two Points Write the equation of the line passing through (0, 3) and (3, 5). Step 1: Step 2: Using the slope and one point (3, 5) write the equation in the slope-intercept form.