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# 2.3 and 2.4 Lines

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• 1. 2.3 LINEAR FUNCTIONS AND SLOPE-INTERCEPT FORM 2.4 MORE ABOUT LINEAR EQUATIONS
• 2. LINEAR FUNCTIONS
• A linear function is a function whose graph is a line.
• We represent a linear function with a linear equation .
• 3. INTERCEPTS
• An intercept of a line is a point where a line crosses an axis.
• The y-intercept is the point at which the line crosses the y-axis.
• The x-intercept is the point at which the line crosses the x-axis.
• 4. TO FIND THE INTERCEPTS
• Set x = 0 and solve for y
• Set y = 0 and solve for x
• List your solutions as ordered pairs
• 5. EXAMPLE: WHAT ARE THE INTERCEPTS OF THE EQUATION?
• 6. SLOPE – INTERCEPT FORM The slope-intercept of an equation of a line is y = mx + b , where m is the slope of the line and (0, b ) is the y -intercept.
• 7. EXAMPLE: WHAT IS AN EQUATION OF THE LINE
• and the y-intercept is
• 8. EXAMPLE: WHAT IS AN EQUATION OF THE LINE
• 9. WORKING WITH LINEAR EQUATIONS
• We can rewrite a linear equation in slope – intercept form by solving for y.
• 10. EXAMPLE: WRITE THE EQUATION IN SLOPE – INTERCEPT FORM. WHAT ARE THE SLOPE AND Y-INTERCEPT.
• 11. EXAMPLE: WRITE THE EQUATION IN SLOPE – INTERCEPT FORM. WHAT ARE THE SLOPE AND Y-INTERCEPT.
• 12. POINT – SLOPE FORM
• Given a point and the slope of a line we can write the equation of the line in point – slope form
• 13. EXAMPLE: WRITING AN EQUATION GIVEN A POINT AND THE SLOPE
• A line passes through with slope
• What is an equation of the line?
• 14. EXAMPLE: WRITING AN EQUATION GIVEN A POINT AND THE SLOPE
• A line passes through with slope
• What is an equation of the line?
• 15. WRITING AN EQUATION GIVEN TWO POINTS
• Find the slope
• Substitute the slope and either point into the point-slope form
• 16. EXAMPLE
• A line passes through (3, 2) and (5, 8). What is an equation of the line in point-slope form?
• 17. STANDARD FORM
• Another form of the equation of a line is standard form .
• The coefficients of x and y and the constant should be intgers
• A should be postive!
• 18. WRITING AN EQUATION IN STANDARD FORM WITH INTEGER COEFFICIENTS
• Isolate the constant
• Eliminate Fractions:
• Multiply each side of the equation by the least common denominator of all fraction coefficients
• 19. EXAMPLE: WRITE THE EQUATION IN STANDARD FORM.
• 20.