INSTRUCTORS Carleen Eaton Grant Fraser Eric Smith

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### Slope Intercept Form of an Equation

• The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept of the graph.
• Given a graph, you can determine the slope and the y-intercept and then write the equation in slope-intercept form.
• If you are given the equation in slope-intercept form, you can use the information given by the equation to draw the graph without the need to create a table of values.
• In most problems involving linear equations and their graphs, you will be asked to find the equation in slope-intercept form.
• If you are given the slope of a line and a point that is not the y-intercept, first find the y-intercept by substituting the coordinates of the point and the given slope into the slope-intercept form and solving for b. Then you have the information necessary to write the equation in slope-intercept form.
• If you are given 2 points that lie on a line, first use their coordinates to find the slope. The follow the procedure just given to find the y-intercept; you can use either point to do this. Then write the equation in slope-intercept form.

### Slope Intercept Form of an Equation

A line passes through the points (5,4) and (0,8). Find the equation of the line in slope intercept form.
• y = mx + b
slope = [(y2 − y1)/(x2 − x1)]
• slope = [(8 − 4)/(0 − 5)] = [4/( − 5)]
y = − [4/5]x + 8
A line passes through the points ( - 3,6) and (0, - 6). Find the equation of the line in slope intercept form.
• y = mx + b
slope = [(y2 − y1)/(x2 − x1)]
• slope = [( − 6 − 6)/(0 − ( − 3))]
• slope = [( − 12)/3]
• slope = − 4
y = − 4x − 6
A line has slope - 4 and passes through ( - 10, - 8). Find its equation in slope intercept form.
• y = mx + b
• m = − 4
b = ?
• − 8 = − 4( − 10) + b
• − 8 = 40 + b
• b = − 48
y = − 4x − 48
A line has slope - 1 and passes through (7,15). Find its equation in slope intercept form.
• y = mx + b
• m = − 1
b = ?
• 15 = − 1(7) + b
• 15 = − 7 + b
• 22 = b
• y = − 1x + 22
y = − x + 22
A line passes through the points (4,1) and (0,6). Find the equation of the line in slope intercept form.
• slope = m = [(y2 − y1)/(x2 − x1)]
• m = [(6 − 1)/(0 − 4)]
• m = [5/( − 4)]
• y = mx + b
y = − [5/4]x + 6
A line has slope - 7 and passes through ( - 8,11). Find its equation in slope intercept form.
• y = mx + b
• m = − 7
b = ?
• 11 = − 7( − 8) + b
• 11 = 56 + b
• − 45 = b
y = − 7x − 45
A line passes through the points ( - 2, - 3) and (4, - 2). Find the equation of this line in slope intercept form.
• m = [(y2 − y1)/(x2 − x1)]
• m = [( − 2 − ( − 3))/(4 − ( − 2))]
• m = [1/6]
• y = mx + b
• − 3 = [1/6]( − 2) + b
• − 3 = − [2/6] + b
• − 2[4/6] = b
y = [1/6]x − 2[4/6]
A line passes through the points (5, - 4) and ( - 1,6). Find the equation of this line in slope intercept form.
• m = [(y2 − y1)/(x2 − x1)]
• m = [(6 − ( − 4))/( − 1 − 5)]
• m = − [10/6] = − [5/3]
• 6 = − [5/3]( − 1) + b
• 6 = 1[2/3] + b
4[1/3] = b
Graph y = 3x − 5
• Identify slope
• m = 3
• Identify intercept
• b = − 5
Graph utilizing slope and intercept
Graph y = [x/2] + 3
• Identify slope
• m = [1/2]
• Identify intercept
• b = 3
Graph utilizing slope and intercept

*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.