Equation of a straight line questions with answers

Questions

1. Question 1Gradient and y-intercept

   Find the equation of the line with gradient $3$ that passes through $(0, 2)$.

   Show the worked solution

   1. Step 1: Read off the gradient$m = 3$
   2. Step 2: The line crosses the y-axis at (0, c)$c = 2$
   3. Step 3: Write the equation$y = 3x + 2$
2. Question 2Gradient and a point

   Find the equation of the line with gradient $2$ that passes through $(2, 6)$.

   Show the worked solution

   1. Step 1: Read off the gradient$m = 2$
   2. Step 2: Substitute the point into y = mx + c$6 = 2(2) + c$$c = 2$
   3. Step 3: Write the equation$y = 2x + 2$
3. Question 3Two points

   Find the equation of the line passing through $A(3, -3)$ and $B(4, 6)$.

   Show the worked solution

   1. Step 1: Find the gradient: put the coordinates into the gradient formula$m = \dfrac{y_2 - y_1}{x_2 - x_1}$$m = \dfrac{6 - (-3)}{4 - 3}$$\phantom{m} = 9$
   2. Step 2: Substitute A into y = mx + c$-3 = 9(3) + c$$c = -30$
   3. Step 3: Write the equation$y = 9x - 30$
4. Question 4Two points, fraction gradient

   Find the equation of the line passing through $A(0, 2)$ and $B(-3, 6)$.

   Show the worked solution

   1. Step 1: Find the gradient: put the coordinates into the gradient formula$m = \dfrac{y_2 - y_1}{x_2 - x_1}$$m = \dfrac{6 - 2}{-3 - 0}$$\phantom{m} = -\dfrac{4}{3}$
   2. Step 2: Substitute A into y = mx + c$2 = -\dfrac{4}{3}(0) + c$$c = 2$
   3. Step 3: Write the equation$y = -\dfrac{4}{3}x + 2$