Straight Line Graphs

• What is the general form of the equation of a straight line?

  y = mx + c
• What do the variables m and c represent in the equation y = mx + c?

  m is the gradient, c is the y-intercept
• How can the equation of a straight line also be expressed?

  ax + by + c = 0
• In the equation ax + by + c = 0, what are a, b, and c?

  They are integers
• Why is finding where lines intercept the coordinate axes important?

  It helps in graphing the lines accurately
• What is the gradient of the line represented by the equation y = 2x + 7?


  2
• What is the y-intercept of the line y = 2x + 7?


  7
• Where does the line y = 2x + 7 cross the coordinate axes?

  At (0, 7) and (-3.5, 0)
• What is the gradient of the line represented by the equation y = -5x - 6?

  • 5
• What is the y-intercept of the line y = -5x - 6?

  • 6
• Where does the line y = -5x - 6 cross the coordinate axes?

  At (0, -6) and (-1.2, 0)
• What is the formula to find the midpoint between two points (x1, y1) and (x2, y2)?

  Midpoint = ((x1 + x2)/2, (y1 + y2)/2)
• What is the formula for the gradient m of a line joining two points?

  m = (y2 - y1) / (x2 - x1)
• Why is it important to find the intercepts of a line?

  It helps in accurately graphing the line
• What is the equation of a straight line in slope-intercept form?

  y = mx + c
• What do the variables m and c represent in the equation y = mx + c?

  m is the gradient, c is the y-intercept
• How can the equation of a straight line also be expressed?

  ax + by + c = 0
• In the equation ax + by + c = 0, what are a, b, and c?

  They are integers
• Why is finding where lines intercept the coordinate axes important?

  It is an important skill in graphing
• What is the gradient of the line represented by the equation y = 2x + 3?


  2
• What is the y-intercept of the line y = 2x + 3?

  3
• How do you find where the line y = 2x + 7 crosses the coordinate axes?

  Set y to 0 for x-intercept, x to 0 for y-intercept
• What is the gradient of the line y = -5x - 6?

  • 5
• What is the y-intercept of the line y = -5x - 6?

  • 6
• What is the gradient of the line y = x + 3.5?

  1
• What is the y-intercept of the line y = x + 3.5?

  1. 5
• How can the equation 3y = 2x + 6 be rewritten in slope-intercept form?

  y = (2/3)x + 2
• What is the gradient of the line represented by the equation 3y = 2x + 6?

  $\frac{2}{3}$
• What is the y-intercept of the line represented by the equation 3y = 2x + 6?


  2
• How can the equation 2x + 4y - 7 = 0 be rewritten in slope-intercept form?

  y = -\frac{1}{2}x + \frac{7}{4}
• What is the gradient of the line represented by the equation 2x + 4y - 7 = 0?

  • $\frac{1}{2}$
• What is the y-intercept of the line represented by the equation 2x + 4y - 7 = 0?

  $\frac{7}{4}$
• How can the equation 3x - y - 6 = 0 be rewritten in slope-intercept form?

  y = 3x - 6
• What is the gradient of the line represented by the equation 3x - y - 6 = 0?

  3
• What is the y-intercept of the line represented by the equation 3x - y - 6 = 0?

  • 6
• How can a straight line be defined using different information?

  • One point on the line and the gradient
  • Two different points on the line

  
• What is the equation of a line with gradient 3 passing through (0, 5)?

  y = 3x + 5

  
• What is the equation of a line with gradient 2 passing through (2, 8)?

  y = 2x + 4
• What is the equation of a line with gradient -$\frac{1}{2}$ passing through (3, -4)?


  y = -\frac{1}{2}x - \frac{5}{2}
• What is the equation of a line with gradient $\frac{3}{4}$ passing through (-2, -7)?


  y = \frac{3}{4}x - \frac{9}{2}