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## Slope-intercept Form

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**Slope-intercept Form**y = mx + b**An equation whose graph is a straight line is a linear**equation. Since a function rule is an equation, a function can also be linear. m = slope b = y-intercept Y = mx + b (if you know the slope and where the line crosses the y-axis, use this form) Slope-intercept Form**For example in the equation;y = 3x + 6m = 3, so the slope is**3b = +6, so the y-intercept is +6 Let’s look at another: y = 4/5x -7 m = 4/5, so the slope is 4/5 b = -7, so the y-intercept is -7 Please note that in the slope-intercept formula; y = mx + b the “y” term is all by itself on the left side of the equation. That is very important!**WHY?If the “y” is not all by itself, then we must first**use the rules of algebra to isolate the “y” term.For example in the equation: 2y = 8x + 10 You will notice that in order to get “y” all by itself we have to divide both sides by 2. After you have done that, the equation becomes: Y = 4x + 5 Only then can we determine the slope (4), and the y-intercept (+5)**OK…getting back to the lesson…Your job is to write the**equation of a line after you are given the slope and y-intercept… Let’s try one… Given “m” (the slope remember!) = 2 And “b” (the y-intercept) = +9 All you have to do is plug those values into y = mx + b The equation becomes… y = 2x + 9**Let’s do a couple more to make sure you are expert at**this. Given m = 2/3, b = -12, Write the equation of a line in slope-intercept form. Y = mx + b Y = 2/3x – 12 ************************* One last example… Given m = -5, b = -1 Write the equation of a line in slope-intercept form. Y = mx + b Y = -5x - 1**Given the slope and y-intercept, write the equation of a**line in slope-intercept form. 1) m = 3, b = -14 2) m = -½, b = 4 3) m = -3, b = -7 4) m = 1/2 , b = 0 5) m = 2, b = 4 Slope-intercept form of an equation Y = mx + b**Using slope-intercept form to find slopes and**y-interceptsThe graph at the right shows the equation of a line both in standard form and slope-intercept form.You must rewrite the equation 6x – 3y = 12 in slope-intercept to be able to identify the slope and y-intercept.**3x – y = 14**-y = -3x + 14 -1 -1 -1 y = 3x – 14 or 3x – y = 14 3x = y + 14 3x – 14 = y x + 2y = 8 2y = -x + 8 2 2 2 y = -1x + 4 2 Using slope-intercept form to write equations, Rewrite the equation solving for y = to determine the slope and y-intercept.**Write each equation in slope-intercept form.Identify the**slope and y-intercept. 2x + y = 10 -4x + y = 6 4x + 3y = 9 2x + y = 3 5y = 3x**1) Find the slope.**4 – (-4)8 -1 – 3 -4 m = -2 2) Choose either point and substitute. Solve for b. y = mx + b (3, -4) -4 = (-2)(3) + b -4 = -6 + b 2 = b Substitute m and b in equation. Y = mx + b Y = -2x + 2 Write the equation of a line in slope-intercept form that passes through points (3, -4) and (-1, 4). Do you remember the slope formula?**Write the equation of the line in slope-intercept form that**passes through each pair of points. • (-1, -6) and (2, 6) • (0, 5) and (3, 1) • (3, 5) and (6, 6) • (0, -7) and (4, 25) • (-1, 1) and (3, -3)