<p> Standard Form</p><p>P re - R e q ui si te 8.EE.5 Graph proportional relationships, interpreting the unit rate as the slope of the St graph. Compare two different proportional relationships represented in different a ways. n d 8.EE.6 Use similar triangles to explain why the slope m is the same between any two ar distinct points on a non-vertical line in the coordinate plane, derive the equation d y=mx for a line through the origin and the equation y = mx + b of a line intercepting the vertical axis at b. C 8.4.19 - 21 C 8.2.23 L e ss o n St  Students graph linear equations on the coordinate plane. u  Students write the equation of a line given two points or the slope and a point on d the line. e n  Students know the traditional forms of the slope formula and slope-intercept t equation. L e ar ni n g G o al M e di a Standard Form</p><p>H #65 W Spiral Review #19 W K S P Standard Form</p><p>Graph 5x + 4y = 8 by completing the following table of values. x 5x + 4y = 8 y</p><p>- 4</p><p>-8</p><p>Solution</p><p>Use x = 2 and x = -2 to find two solutions to the equation 5x + 4y = 8. </p><p>Is the point (4, 3) on the line?</p><p>Is the point (4, -3) on the line? Standard Form</p><p>Intercepts</p><p>The y-axis occurs at x = 0. Hence, to find the y-intercept of a linear equation, substitute the x with 0.</p><p>Find the y-intercept of 5x + 4y = 8.</p><p>The graph of 5x + 4y = 8 will cross the y-axis at ___.</p><p>The x-axis occurs at y = 0. Hence, to find the x-intercept of a linear equation, substitute the y with 0.</p><p>Find the x-intercept of 5x + 4y = 8.</p><p>The graph of 5x + 4y = 8 will cross the x-axis at ___. Standard Form</p><p>Exercise: Graph the following equations by using their intercepts.</p><p>1 x + y = 4 2. -3x + 8y = 24 . x-intercept: (___, 0) x-intercept:</p><p> y-intercept: (0, ___) y-intercept:</p><p>3 x – 3y = 9 4. -3x - 7y = 21 . x-intercept: x-intercept:</p><p> y-intercept: y-intercept: Standard Form</p><p>Write the Equation</p><p>We’ve learned how to write an equation of a graph in slope-intercept form.</p><p>We can now transform the slope-intercept form of an equation into standard form.</p><p>Slope-Intercept form Standard form y = mx + b ax + by = c</p><p>Exercise: Write the equation that represents the following.</p><p>1 slope-intercept form: . standard form:</p><p>2 m = -2 and (0, 3) slope-intercept form: . standard form: Standard Form</p><p>Sometimes you’ll have the blast the equation with a common denominator to get integer coefficients for x and y.</p><p>Slope-Intercept form Standard form y = mx + b ax + by = c</p><p>Exercise: Write the equation that represents the following.</p><p>3. m = and (0, -7) slope-intercept form:</p><p> standard form:</p><p>4. (0, 4) and (5, 6) slope-intercept form:</p><p> standard form: Standard Form</p><p>Remember, the y and the x can be substituted by any point on the line. </p><p>Slope-Intercept form Standard form y = mx + b ax + by = c</p><p>Exercise: Write the equation that represents the following.</p><p>5 (-7, 1) and (4, 0) slope-intercept form: .</p><p> standard form:</p><p>6 (-4, 5) and (2, 3) slope-intercept form: .</p><p> standard form: Standard Form</p><p>Name: ______Date: ______Pre-Algebra Exit Ticket</p><p>Graph the equation y = x – 10 using the y-intercept and slope.</p><p>Graph the equation 5x – 4y = 40 using intercepts.</p><p>What can you conclude about the equations y = x – 10 and 5x – 4y = 40? Standard Form</p><p>Name: ______Date: _____ Pre-Algebra HW #65</p><p>1. Graph x + 3y = 9 by using it’s intercepts.</p><p>Review: 2 Find the equation of the following graph. . </p><p>3 Last summer, a family took a trip to a beach that was about 200 miles away from . their home. The graph below shows the distance driven, in miles, and the time, in hours, taken for the trip. Standard Form</p><p>What was their average speed from hour 1 to hour 4? A. 25 miles per hour B. miles per hour C. miles per hour D. 100 miles per hour</p>